graphical models for marked point processes based on local independence summary a new class of graphical models capturing the dependence structure of events that occur in time is proposed the graphs represent so called local independences meaning that the intensities of certain types of events are independent of some but not necessarilly all events in the past this dynamic concept of independence is asymmetric similar to granger non causality so the corresponding local independence graphs differ considerably from classical graphical models hence a new notion of graph separation which is called separation is introduced and implications for the underlying model as well as for likelihood inference are explored benefits regarding facilitation of reasoning about and understanding of dynamic dependences as well as computational simplifications are discussed

performance analysis for a changepoint problem nonlinear stochastic differential equations are used to model a version of the changepoint problem state estimates of the minimum mean square error type are used in likelihood ratio tests to detect the time of change system performance is evaluated by deriving theoretical expressions for the false alarm probability and a special case of the miss error probability the approach uses a fokker planck equation

on the periodic schrodinger boussinesq system abstract we study the local and global well posedness of the periodic boundary value problem for the nonlinear schrodinger boussinesq system the existence of periodic traveling wave solutions as well as the orbital stability of such solutions are also considered

existence of solutions to the convection problem in a pseudomeasure type space we study the well posedness of a convection problem in a pseudomeasure type space pma without assuming that the gravitational field is bounded considering the pma space with right homogeneity th

relative entropy exponential utility and robust dynamic pricing in the area of dynamic revenue management optimal pricing policies are typically computed on the basis of an underlying demand rate model from the perspective of applications this approach implicitly assumes that the model is an accurate representation of the real world demand process and that the parameters characterizing this model can be accurately calibrated using data in many situations neither of these conditions are satisfied indeed models are usually simplified for the purpose of tractability and may be difficult to calibrate because of a lack of data moreover pricing policies that are computed under the assumption that the model is correct may perform badly when this is not the case this paper presents an approach to single product dynamic revenue management that accounts for errors in the underlying model at the optimization stage uncertainty in the demand rate model is represented using the notion of relative entropy and a tractable reformulation of the robust pricing problem is obtained using results concerning the change of probability measure for point processes the optimal pricing policy is obtained through a version of the so called isaacs equation for stochastic differential games and the structural properties of the optimal solution are obtained through an analysis of this equation in particular i closed form solutions for the special case of an exponential nominal demand rate model ii general conditions for the exchange of the max and the min in the differential game and iii the equivalence between the robust pricing problem and that of single product revenue management with an exponential utility function without model uncertainty are established through the analysis of this equation

bootstrap and permutation tests of independence for point processes motivated by a neuroscience question about synchrony detection in spike train analysis we deal with the independence testing problem for point processes we introduce non parametric test statistics which are rescaled general u statistics whose corresponding critical values are constructed from bootstrap and randomization permutation approaches making as few assumptions as possible on the underlying distribution of the point processes we derive general consistency results for the bootstrap and for the permutation w r t to wasserstein s metric which induce weak convergence as well as convergence of second order moments the obtained bootstrap or permutation independence tests are thus proved to be asymptotically of the prescribed size and to be consistent against any reasonable alternative a simulation study is performed to illustrate the derived theoretical results and to compare the performance of our new tests with existing ones in the neuroscientific literature

effects of attachment preferences on coevolution of opinions and networks abstract in the coevolution of network structures and opinion formation we investigate the effects of a mixed population with distinctive relinking preferences on both the convergence time and the network structures it has been found that a heterogeneous network structure is easier to be reached with more high degree preferential hdp nodes there exists high correlation between the convergence time and the network heterogeneity the heterogeneous degree distribution caused by preferential attachment accelerates the convergence to a consensus state and the shortened convergence time inhibits the occurrence of the following disquieting situation that occurs in a continuously evolving network with preferential attachment and long time evolvement most of the nodes would become separated and only a few leaders would have immediate neighbors analytical calculations based on mean field theory reveal that both the transition point p t r and the consensus time depend upon the standard deviation of the degree distribution d p t r increases while decreases with the rise of d functions of p t r k k 1 and a n k d 2 k are found theoretical analyses are in accordance with simulation data

self similarity and asymptotic stability for coupled nonlinear schrodinger equations in high dimensions abstract this paper is concerned with systems of coupled schrodinger equations with polynomial nonlinearities and dimension n 1 we show the existence of global self similar solutions and prove that they are asymptotically stable in a framework based on weak l p spaces whose elements have local finite l 2 mass the radial symmetry of the solutions is also addressed

a characterization of the spatial poisson process and changing time watanabe proved that if x t is a point process such that x t t is a martingale then x t is a poisson process and this result was generalized by bremaud for doubly stochastic poisson processes here we define two parameter point processes and extend this property without needing the strong martingale condition using this characterization we study the problem of transforming a two parameter point process into a two parameter poisson process by means of a family of stopping lines as a time change nualart and sanz gave conditions in order to transform a square integrable strong martingale into a wiener process here we do the same for the poisson process by a similar method but under more general conditions

strong convergence for split step methods in stochastic jump kinetics mesoscopic models in the reaction diffusion framework have gained recognition as a viable approach to describing chemical processes in cell biology the resulting computational problem is a continuous time markov chain on a discrete and typically very large state space due to the many temporal and spatial scales involved many different types of computationally more effective multiscale models have been proposed typically coupling different types of descriptions within the markov chain framework in this work we look at the strong convergence properties of the basic first order strang or lie trotter split step method which is formed by decoupling the dynamics in finite time steps thanks to its simplicity and flexibility this approach has been tried in many different combinations we develop explicit sufficient conditions for pathwise well posedness and convergence of the method including error estimates and we illustrate our findings with numerical examples in doing so we also suggest a certain

a multiplicative seasonal component in commodity derivative pricing abstract in this paper we focus on a seasonal jump diffusion model to price commodity derivatives we propose a novel approach to estimate the functions of the risk neutral processes directly from data in the market even when a closed form solution for the model is not known then this new approach is applied to price some natural gas derivative contracts traded at new york mercantile exchange nymex moreover we use nonparametric estimation techniques in order to avoid arbitrary restrictions on the model after applying this approach we find that a jump diffusion model allowing for seasonality outperforms a standard jump diffusion model to price natural gas futures furthermore we also show that there are considerable differences in the option prices and the risk premium when we consider seasonality or not these results have important implications for practitioners in the market

reputation in continuous time games we study reputation dynamics in continuous time games in which a large player e g government faces a population of small players e g households and the large player s actions are imperfectly observable the major part of our analysis examines the case in which public signals about the large player s actions are distorted by a brownian motion and the large player is either a normal type who plays strategically or a behavioral type who is committed to playing a stationary strategy we obtain a clean characterization of sequential equilibria using ordinary differential equations and identify general conditions for the sequential equilibrium to be unique and markovian in the small players posterior belief we find that a rich equilibrium dynamics arises when the small players assign positive prior probability to the behavioral type by contrast when it is common knowledge that the large player is the normal type every public equilibrium of the continuous time game is payoff equivalent to one in which a static nash equilibrium is played after every history finally we examine variations of the model with poisson signals and multiple behavioral types

decoding movement trajectories through a t maze using point process filters applied to place field data from rat hippocampal region ca1 firing activity from neural ensembles in rat hippocampus has been previously used to determine an animal s position in an open environment and separately to predict future behavioral decisions however a unified statistical procedure to combine information about position and behavior in environments with complex topological features from ensemble hippocampal activity has yet to be described here we present a two stage computational framework that uses point process filters to simultaneously estimate the animal s location and predict future behavior from ensemble neural spiking activity first in the encoding stage we linearized a two dimensional t maze and used spline based generalized linear models to characterize the place field structure of different neurons all of these neurons displayed highly specific position dependent firing which frequently had several peaks at multiple locations along the maze when the rat was at the stem of the t maze the firing activity of several of these neurons also varied significantly as a function of the direction it would turn at the decision point as detected by anova second in the decoding stage we developed a state space model for the animal s movement along a t maze and used point process filters to accurately reconstruct both the location of the animal and the probability of the next decision the filter yielded exact full posterior densities that were highly nongaussian and often multimodal our computational framework provides a reliable approach for characterizing and extracting information from ensembles of neurons with spatially specific context or task dependent firing activity

smoothing point processes as a means to increase throughput unlike the leaky bucket scheme which regulates the input rate the filters we study in this paper reduce the variability of interarrival times subject to a maximum delay constraint for each customer these filters are called smoothing filters for point processes by considering the output processes of various queueing systems we show that an infinite server queue acts as a smoothing filter for a doubly stochastic poisson process and a single server queue with deterministic service times acts as a smoothing filter for a stationary and ergodic point process based on the second point we provide a smoothing algorithm that satisfies a maximum delay constraint the algorithm is shown to be robust and consistent we then consider two examples where these filters can be applied to increase throughput one is the single server loss system with exponential service times the other is the leaky bucket scheme with token buffer size 1 numerical examples and simulations are also given for comparing the tradeoff between delay and throughput our approach is based on the variability ordering and a cut criterion for the majorization ordering the criterion appears to be new and of independent interest

numerical solution of stochastic quantum master equations using stochastic interacting wave functions abstract we develop a new approach for solving stochastic quantum master equations with mixed initial states first we obtain that the solution of the jump diffusion stochastic master equation is represented by a mixture of pure states satisfying a system of stochastic differential equations of schrodinger type then we design three exponential schemes for these coupled stochastic schrodinger equations which are driven by brownian motions and jump processes hence we have constructed efficient numerical methods for the stochastic master equations based on quantum trajectories the good performance of the new numerical integrators is illustrated by simulations of two quantum measurement processes

coevolution of glauber like ising dynamics and topology we study the coevolution of a generalized glauber dynamics for ising spins with tunable threshold and of the graph topology where the dynamics takes place this simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model the threshold and the rewiring probability the diagram displays phase transitions of different types spin ordering percolation and connectedness at variance with traditional coevolution models in which all spins of each connected component of the graph have equal value in the stationary state we find that for suitable choices of the parameters the system may converge to a state in which spins of opposite sign coexist in the same component organized in compact clusters of like signed spins mean field calculations enable one to estimate some features of the phase diagram

flows in queueing networks a martingale approach this paper applies the filtering theory for point process observations to the analysis of flows in networks an abstract model for the study of markovian queueing systems is developed and used to derive the filtering equations satisfied by the conditional probability distribution of the state given the past of an observed set of flows these filtering equations are used to obtain a necessary and sufficient condition for that observation to be independent of the value of the state of the system at any time this approach also yields a probabilistic interpretation of a necessary condition for a given flow in a multi class jackson network to be poisson these results are combined to give a proof of the loop criterion for single class jackson network and to show that this criterion does not apply to multi class networks examples of loop free jackson networks are given for which some of the flows are not poisson

concentration inequalities for matrix martingales in continuous time this paper gives new concentration inequalities for the spectral norm of a wide class of matrix martingales in continuous time these results extend previously established freedman and bernstein inequalities for series of random matrices to the class of continuous time processes our analysis relies on a new supermartingale property of the trace exponential proved within the framework of stochastic calculus we provide also several examples that illustrate the fact that our results allow us to recover easily several formerly obtained sharp bounds for discrete time matrix martingales

a martingale approach to point processes in the plane on donne une definition rigoureuse des processus ponctuels a deux parametres comme une distribution d une quantite denombrable de points aleatoires du plan on obtient une caracterisation avec des droites d arret et une relation avec la predictibilite

signal processing with levy information levy processes which have stationary independent increments are ideal for modelling the various types of noise that can arise in communication channels if a levy process admits exponential moments then there exists a parametric family of measure changes called esscher transformations if the parameter is replaced with an independent random variable the true value of which represents a message then under the transformed measure the original levy process takes on the character of an information process in this paper we develop a theory of such levy information processes the underlying levy process which we call the fiducial process represents the noise type each such noise type is capable of carrying a message of a certain specification a number of examples are worked out in detail including information processes of the brownian poisson gamma variance gamma negative binomial inverse gaussian and normal inverse gaussian type although in general there is no additive decomposition of information into signal and noise one is led nevertheless for each noise type to a well defined scheme for signal detection and enhancement relevant to a variety of practical situations

exact simulation of point processes with stochastic intensities point processes with stochastic arrival intensities are ubiquitous in many areas including finance insurance reliability health care and queuing they can be simulated from a poisson process by time scaling with the cumulative intensity the paths of the cumulative intensity are often generated with a discretization method however discretization introduces bias into the simulation results the magnitude of the bias is difficult to quantify this paper develops a sampling method that eliminates the need to discretize the cumulative intensity the method is based on a projection argument and leads to unbiased simulation estimators it is exemplified for a point process whose intensity is a function of a jump diffusion process and the point process itself in this setting the method facilitates the exact sampling of both the point process and the driving jump diffusion process numerical experiments demonstrate the effectiveness of the method

mutual information relative entropy and estimation in the poisson channel let be a nonnegative random variable and let the conditional distribution of a random variable given be poisson for a parameter we identify a natural loss function such that 1 the derivative of the mutual information between and with respect to is equal to the minimum mean loss in estimating based on regardless of the distribution of 2 when is estimated based on by a mismatched estimator that would have minimized the expected loss had the integral over all values of of the excess mean loss is equal to the relative entropy between and for a continuous time setting where is a nonnegative stochastic process and the conditional law of given is that of a non homogeneous poisson process with intensity function under the same loss function 1 the minimum mean loss in causal filtering when is equal to the expected value of the minimum mean loss in noncausal filtering smoothing achieved with a channel whose parameter is uniformly distributed between 0 and bridging the two quantities is the mutual information between and 2 this relationship between the mean losses in causal and noncausal filtering holds also in the case where the filters employed are mismatched i e optimized assuming a law on which is not the true one bridging the two quantities in this case is the sum of the mutual information and the relative entropy between the true and the mismatched distribution of thus relative entropy quantifies the excess estimation loss due to mismatch in this setting these results are parallel to those recently found for the gaussian channel the i mmse relationship of guo the relative entropy and mismatched estimation relationship of verdu and the relationship between causal and noncasual mismatched estimation of weissman

self organized scale free networks growth and preferential attachments have been coined as the two fundamental mechanisms responsible for the scale free feature in complex networks as characterized by an algebraic degree distribution there are situations particularly in biological networks where growth is absent or not important yet some of these networks still exhibit the scale free feature with a small degree exponent here we propose two classes of models to account for this phenomenon we show analytically and numerically that in the first model a spectrum of algebraic degree distributions with a small exponent can be generated the second model incorporates weights for nodes and it is able to generate robust scale free degree distribution with larger algebraic exponents our results imply that it is natural for a complex network to self organize itself into a scale free

consensus formation on coevolving networks groups formation and structure we study the effect of adaptivity on a social model of opinion dynamics and consensus formation we analyse how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups and the convergence time to the stable final state we find that while on static networks these properties are determined by percolation phenomena on adaptive networks the rewiring process leads to different behaviors adaptive rewiring fosters group formation by enhancing communication between agents of similar opinion though it also makes possible the division of clusters we show how the convergence time is determined by the characteristic time of link rearrangement we finally investigate how the adaptivity yields nontrivial correlations between the internal topology and the size of the groups of agreeing agents

on the drawdowns and drawups in diffusion type models with running maxima and minima we obtain closed form expressions for the values of joint laplace transforms of the running maximum and minimum of a diffusion type process stopped at the first time at which the associated drawdown and drawup processes hit constant levels it is assumed that the coefficients of the diffusion type process are regular functions of the running values of the process itself its maximum and minimum as well as its maximum drawdown and maximum drawup processes the proof is based on the solution to the equivalent boundary value problems and application of the normal reflection conditions for the value functions at the edges of the state space of the resulting five dimensional markov process we show that the joint laplace transforms represent linear combinations of solutions to the systems of first order partial differential equations arising from the application of the normal reflection conditions

methods for the analysis of sampled cohort data in the cox proportional hazards model methods are provided for regression parameter and cumulative baseline hazard estimation in the cox proportional hazards model when the cohort is sampled according to a predictable sampling probability law the key to the methodology is to define counting processes which count joint failure and sampled risk sets occurrences and to derive the appropriate intensities for these counting processes leading to estimation methods parallel to those for full cohort data these techniques are illustrated for a number of sampling designs including three novel designs counter matching with additional randomly sampled controls quota sampling of controls and nested case control sampling with number of controls dependent on the failure s exposure status general asymptotic theory is developed for the maximum partial likelihood estimator and cumulative baseline hazard estimator and is used to derive the asymptotic distributions for estimators from a large class of designs

filtering a markov modulated random measure we develop a new exact filter when a hidden markov chain influences both the sizes and times of a marked point process an example would be an insurance claims process where we assume that both the stochastic intensity of the claim arrivals and the distribution of the claim sizes depend on the states of an economy we also develop the robust filter based and smoother based em algorithms for the on line recursive estimates of the unknown parameters in the markov modulated random measure our development is in the framework of modern theory of stochastic processes

an anti pasta result for markovian systems pasta poisson arrivals see time averages is a term coined by r wolff in his well known 1982 paper in keeping with wolff s terminology we use the term anti pasta to refer to the following converse of pasta given that arrivals do indeed see time averages when must the arrival process necessarily be poisson we show that anti pasta is satisfied in a pure jump markov process provided that the arrival process corresponds to a subset of the markov process jumps

closed form likelihood approximation and estimation of jump diffusions with an application to the realignment risk of the chinese yuan this paper provides closed form likelihood approximations for multivariate jump diffusion processes widely used in finance for a fixed order of approximation the maximum likelihood estimator mle computed from this approximate likelihood achieves the asymptotic efficiency of the true yet uncomputable mle as the sampling interval shrinks this method is used to uncover the realignment probability of the chinese yuan since february 2002 the market implied realignment intensity has increased fivefold the term structure of the forward realignment rate which completely characterizes future realignment probabilities is hump shaped and peaks at mid 2004 the realignment probability responds quickly to economic news releases and government interventions r 2007 elsevier b v all rights reserved

on galerkin approximations for the zakai equation with diffusive and point process observations this paper studies galerkin approximations applied to the zakai equation of stochastic filtering the basic idea of this approach is to project the infinite dimensional zakai equation onto some finite dimensional subspace generated by smooth basis functions this leads to a finite dimensional system of stochastic differential equations that can be solved numerically the contribution of the paper is twofold on the theoretical side existing convergence results are extended to filtering models with observations of point process or mixed type on the applied side various issues related to the numerical implementation of the method are considered in particular we propose working with a subspace that is constructed from a basis of hermite polynomials the paper closes with a numerical case study

exact solution for the time evolution of network rewiring models we consider the rewiring of a bipartite graph using a mixture of random and preferential attachment the full mean field equations for the degree distribution and its generating function are given the exact solution of these equations for all finite parameter values at any time is found in terms of standard functions it is demonstrated that these solutions are an excellent fit to numerical simulations of the model we discuss the relationship between our model and several others in the literature including examples of urn backgammon and balls in boxes models the watts and strogatz rewiring problem and some models of zero range processes our model is also equivalent to those used in various applications including cultural transmission family name and gene frequencies glasses and wealth distributions finally some voter models and an example of a minority game also show features described by our model

zero rate reliability of the exponential server timing channel we determine the reliability function of the exponential server timing channel estc in the limit as the data rate approaches zero the limit shows that at low rates the estc is strictly more reliable than the poisson channel without dark current answering a question arikan posed in these transactions the proof employs a distance metric over inputs to timing channels that parallels euclidean and hamming distance for conventional channels a consequence of the proof is that bounded distance decoding with distance measured according to this metric is exponentially optimum for the estc in the low rate regime we also prove the straight line bound for the channel and a bound on the reliability of timing channels with general service distributions in the limit as the data rate approaches zero

specification diagnostics for duration models a martingale approach abstract this paper develops specification diagnostics for discrete time duration models which are based on the martingale theory of stochastic processes the methods can be applied to parametric grouped data duration models with time varying covariates right censoring and which account for unobserved heterogeneity a residual process is defined such that under the correct model specification the process is approximately a martingale difference sequence chi square tests based on these residuals are derived results from monte carlo simulations are presented

renewal theory properties of ion channels this paper uses a type of data to attack the problem of deciding whether or not the channels in a membrane are operating independently and if so estimating the distribution of the sojourn periods in emitting and nonomitting states

scale free topology induced double resonance in networked two state systems we study numerically the effect of a scale free topology on the signal to noise ratio of networked two state systems and find a double resonance phenomenon i e a resonance on coupling strength and a stochastic resonance on noise strength this finding suggests an alternative approach of self tuning i e tuning from the scale free topology instead of the self tuning of potential a heuristic theory through a starlike network is presented to explain the double resonance

system size stochastic resonance in a model for opinion formation we study a model for opinion formation which incorporates three basic ingredients for the evolution of the opinion held by an individual imitation influence of fashion and randomness we show that in the absence of fashion the model behaves as a bistable system with random jumps between the two stable states with a distribution of times following kramer s law we also demonstrate the existence of system size stochastic resonance by which there is an optimal value for the number of individuals n for which the average opinion follows better the fashion

multidimensional residual analysis of point process models for earthquake occurrences residual analysis methods for examining the fit of multidimensional point process models are applied to point process models for the space time magnitude distribution of earthquake occurrences using in particular the multidimensional version of ogata s epidemic type aftershock sequence etas model and a 30 year catalog of 580 earthquakes occurring in bear valley california one method involves rescaled residuals obtained by transforming points along one coordinate to form a homogeneous poisson process inside a random irregular boundary another method involves thinning the point process according to the conditional intensity to form a homogeneous poisson process on the original untransformed space the thinned residuals suggest that the fit of the model may be significantly improved by using an anisotropic spatial distance function in the estimation of the spatially varying background rate using rescaled residuals it is shown that the temporal magnitude distribution of aftershock activity is not

a probabilistic look at networks of quasi reversible queues probabilistic arguments are given to explain some recent results on networks of queues those results are the product form the output theorems the distributions at the jumps and the poisson character of the flows the proposed approach replaces the usual calculations by arguments showing these properties to be consequences of the behavior of the nodes in isolation

trees under attack a ray knight representation of feller s branching diffusion with logistic growth we obtain a representation of feller s branching diffusion with logistic growth in terms of the local times of a reflected brownian motion h with a drift that is affine linear in the local time accumulated by h at its current level as in the classical ray knight representation the excursions of h are the exploration paths of the trees of descendants of the ancestors at time t 0 and the local time of h at height t measures the population size at time t we cope with the dependence in the reproduction by introducing a pecking order of individuals an individual explored at time s and living at time t h s is prone to be killed by any of its contemporaneans that have been explored so far the proof of our main result relies on approximating h with a sequence of harris paths h n which figure in a ray knight representation of the total mass of a branching particle system we obtain a suitable joint convergence of h n together with its local times and with the girsanov densities that introduce the dependence in the reproduction

brief paper optimization of queuing system via stochastic control the problem of access and service rate control in queuing systems as a general optimization problem for controlled markov process with finite state space is considered by using the dynamic programming approach we obtain the explicit form of the optimal control in the case of minimizing cost given as a mixture of an average queue length number of lost jobs and service resources the problem is considered on a finite time interval in the case of nonstationary input flow in this case we suggest the general procedure of the numerical solution which can be applied to a problems with constraints

pricing vulnerable power exchange options in an intensity based framework abstract in this article we study the valuation of a european vulnerable power exchange option in an intensity based framework we assume that the default by the counter party is the time of the first jump of a doubly stochastic poisson process whose intensity is modeled by a jump diffusion process the dynamics of the two assets are assumed to be driven by correlated jump diffusion processes all the three processes are assumed to be correlated in continuous part as well as in the jump part in the proposed framework employing the measure change technique we obtain the explicit formula for the price of the power exchange option with counter party risk furthermore sensitivity analysis is given to illustrate the effects of counterparty risk on the price of the option and effect of various parameters on the option prices

on arrivals that see time averages we investigate when arrivals see time averages asta in a stochastic model i e when the stationary distribution of an embedded sequence obtained by observing a continuous time stochastic process just prior to the points arrivals of an associated point process coincides with the stationary distribution of the observed process we also characterize the relation between the two distributions when asta does not hold we introduce a lack of bias assumption lba which stipulates that at any time the conditional intensity of the point process given the present state of the observed process be independent of the state of the observed process we show that lba without the poisson assumption is necessary and sufficient for asta in a stationary process framework consequently lba covers known examples of non poisson asta such as certain flows in open jackson queueing networks as well as the familiar poisson case pasta we also establish results to cover the case in which the process is observed just after the points e g when departures see time averages finally we obtain a new proof of the arrival theorem for product form queueing networks

asymptotic control for a class of piecewise deterministic markov processes associated to temperate viruses we aim at characterizing the asymptotic behavior of value functions in the control of piecewise deterministic markov processes pdmp of switch type under nonexpansive assumptions for a particular class of processes inspired by temperate viruses we show that uniform limits of discounted problems as the discount decreases to zero and time averaged problems as the time horizon increases to infinity exist and coincide the arguments allow the limit value to depend on initial configuration of the system and do not require dissipative properties on the dynamics the approach strongly relies on viscosity techniques linear programming arguments and coupling via random measures associated to pdmp as an intermediate step in our approach we present the approximation of discounted value functions when using piecewise constant in time open loop policies

self organization of complex networks as a dynamical system to understand the dynamics of real world networks we investigate a mathematical model of the interplay between the dynamics of random walkers on a weighted network and the link weights driven by a resource carried by the walkers our numerical studies reveal that under suitable conditions the co evolving dynamics lead to the emergence of stationary power law distributions of the resource and link weights while the resource quantity at each node ceaselessly changes with time we analyze the network organization as a deterministic dynamical system and find that the system exhibits multistability with numerous fixed points limit cycles and chaotic states the chaotic behavior of the system leads to the continual changes in the microscopic network dynamics in the absence of any external random noises we conclude that the intrinsic interplay between the states of the nodes and network reformation constitutes a major factor in the vicissitudes of real world networks

consensus formation on adaptive networks the structure of a network can significantly influence the properties of the dynamical processes that take place on them while many studies have been paid to this influence much less attention has been devoted to the interplay and feedback mechanisms between dynamical processes and network topology on adaptive networks adaptive rewiring of links can happen in real life systems such as acquaintance networks where people are more likely to maintain a social connection if their views and values are similar in our study we consider different variants of a model for consensus formation our investigations reveal that the adaptation of the network topology fosters cluster formation by enhancing communication between agents of similar opinion although it also promotes the division of these clusters the temporal behavior is also strongly affected by adaptivity while on static networks it is influenced by percolation properties on adaptive networks both the early and late time evolutions of the system are determined by the rewiring process the investigation of a variant of the model reveals that the scenarios of transitions between consensus and polarized states are more robust on adaptive networks

on the reliability function of the ideal poisson channel with noiseless feedback a coding scheme for the channel under peak power and average power constraints on the input is presented and its asymptotic error exponent is shown to coincide at all rates below capacity with the sphere packing error exponent which for the case at hand is known to be unachievable without feedback for rates below the critical rate an upper bound on the error exponent achievable with feedback is also derived and shown under a capacity reducing average power constraint to coincide with the error exponent achieved by the proposed coding scheme in such a case the coding scheme is asymptotically optimal thus the ideal poisson channel limited by a capacity reducing average power constraint provides a nontrivial example of a channel for which the reliability function is known exactly both with and without feedback it is shown that a slight modification of the coding scheme to one of random transmission time can achieve zero error probability for any rate lower than the ordinary average error channel capacity

a nonparametric dynamic additive regression model for longitudinal data in this work we study additive dynamic regression models for longitudinal data these models provide a flexible and nonparametric method for investigating the time dynamics of longitudinal data the methodology is aimed at data where measurements are recorded at random time points we model the conditional mean of responses given the full internal history and possibly time varying covariates we derive the asymptotic distribution for a new nonparametric least squares estimator of the cumulative time varying regression functions based on the asymptotic results confidence bands may be computed and inference about time varying coefficients may be drawn we propose two estimators of the cumulative regression function one estimator that involves smoothing and one that does not the latter however has twice the variance as the smoothing based estimator goodness of fit of the model is considered using martingale residuals finally we also discuss how partly conditional mean models in which the mean of the response is regressed onto selected time varying covariates may be analysed in the same framework we apply the methods to longitudinal data on height development for cystic fibrosis patients

on channel capacity per unit cost memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered the maximum number of bits that can be transmitted reliably through the channel per unit cost is studied it is shown that if the input alphabet contains a zero cost symbol then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions the direct part of this coding theorem admits a constructive proof via stein s lemma on the asymptotic error probability of binary hypothesis tests single user multiple access and interference channels are studied

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

optimal control versus stochastic target problems an equivalence result abstract within a general abstract framework we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in soner and touzi 2002 5 whenever the underlying filtered probability space admits a suitable martingale representation property this provides a unified way of treating these two classes of stochastic control problems as an illustration we show within a jump diffusion framework how the hamilton jacobi bellman equations associated to an optimal control problem in standard form can be easily retrieved from the partial differential equations associated to its stochastic target counterpart

performance bounds for mismatched decision schemes with poisson process observations abstract this paper develops a framework for analyzing the performance loss in fixed time interval decision algorithms that are based on observations of time inhomogeneous poisson processes when some parameters characterizing the observation process are not known exactly key to the development is the formulation of an analytically computable performance metric which can be used in lieu of the true but intractable error probabilities the proposed metric is obtained by identifying analytical upper bounds on the error probabilities in terms of the uncertain parameters using these tools it is shown that performance degrades gracefully as long as the true values of the parameters remain within a neighborhood of the nominal values used in decision making the results find direct application to problems of detecting illicit nuclear materials in transit

martingale dynamics and optimal routing in a network in this paper we consider a dynamic routing problem in a store and forward computer communication network which consists of l parallel channels connected between the source and the destination we prove that if messages arrive at the network in accordance with a poisson process and all nodes have an exponential service rate then the routing strategy that minimizes the total expected time in transmitting all messages that arrive before t 0 is to route the arriving message to the channel along which the sum of all queue sizes is minimum techniques of martingale and dynamic programming are used in obtaining the result

performance analysis of an asymptotically quantum limited optical dpsk receiver an optical direct detection differential phase shift keying dpsk receiver whose error probability is quantum limited as the transmitting laser linewidth vanishes is analyzed the receiver design is based on a binary equiprobable hypothesis test with doubly stochastic point process observations the conditional random rates of which depend on the transmitting laser phase noise which is modeled as a brownian motion the receiver structure consists of a simple delay and sum optical preprocessor followed by a photoelectric converter and an integrate and dump circuit upper and lower bounds on the receiver bit error rate are derived by developing bounds on the conditional rates of the point process and it is shown that the error probability bounds converge to the true value as the transmitting laser linewidth decreases bounds on the power penalty are computed for parameters corresponding to existing semiconductor injection lasers and are seen to be less than the limiting power penalty for the balanced dpsk receiver

option pricing with a general marked point process this paper examines the impact of a random number of price changes on the options valuation the model introduces the structure of the general marked point processes mpp this kind of model allows us to take account of more general distributions of interarrival times than usual jump diffusion models in particular stock price variations can be correlated with the times of transactions thus the investors can decide to trade according to the history of market values and the sizes of price variations can also depend on the past times of transactions by using the special decomposition of predictable processes with respect to a marked point process the determination of all risk neutral probabilities is detailed derivative prices are calculated in this context with different basic examples

relative efficiency of the log rank test within a multiplicative intensity model summary for large sample clinical trials with independent individuals randomly allocated to two treatment groups in which survival times follow a log linear multiplicative intensity model with treatment group as one covariate this paper calculates the asymptotic relative efficiency of the log rank test for treatment effect as compared with the optimal score test the method is to exhibit the failure hazard intensity not of proportional hazards form obtained by ignoring all covariates other than treatment group the efficiency formulae are illustrated in two examples and estimation from data of the loss of efficiency is illustrated for two clinical trial datasets

estimation of continuous time markov processes sampled at random time intervals we introduce a family of generalized method of moments estimators of the parameters of a continuous time markov process observed at random time intervals the results include strong consistency asymptotic normality and a characterization of standard errors sampling is at an arrival intensity that is allowed to depend on the underlying markov process and on the parameter vector to be estimated we focus on financial applications including tick based sampling allowing for jump diffusions regime switching diffusions and reflected diffusions

dynamics of opinion formation in a small world network the dynamical process of opinion formation within a model using a local majority opinion updating rule is studied numerically in networks with the small world geometrical property the network is one in which shortcuts are added to randomly chosen pairs of nodes in an underlying regular lattice the presence of a small number of shortcuts is found to shorten the time to reach a consensus significantly the effects of having shortcuts in a lattice of fixed spatial dimension are shown to be analogous to that of increasing the spatial dimension in regular lattices the shortening of the consensus time is shown to be related to the shortening of the mean shortest path as shortcuts are added results can also be translated into that of the dynamics of a spin system in a small world network

convergence of a discretization scheme for jump diffusion processes with state dependent intensities this paper proves a convergence result for a discretization scheme for simulating jump diffusion processes with state dependent jump intensities with a bound on the intensity the point process of jump times can be constructed by thinning a poisson random measure using state dependent thinning probabilities between the jump epochs of the poisson random measure the dynamics of the constructed process are purely diffusive and may be simulated using standard discretization methods under conditions on the coefficient functions of the jump diffusion process we show that the weak convergence order of this method equals the weak convergence order of the scheme used for the purely diffusive intervals the construction of jumps does not degrade the convergence of the method

jump diffusion processes in random environments abstract in this paper we investigate jump diffusion processes in random environments which are given as the weak solutions of sdes we formulate conditions ensuring existence and uniqueness in law of solutions we investigate the markov property to prove uniqueness we solve a general martingale problem for cadlag processes this result is of independent interest application of our results to generalized exponential levy model are present in the last section

existence and scattering theory for boussinesq type equations with singular data we study the initial value problem for the generalized boussinesq equation and prove existence of local and global solutions with singular initial data in weak lp spaces our class of initial data for global existence is larger than that of cho and ozawa 2007 7 long time behavior results are obtained and a scattering theory is proved in that framework with more structure we show sobolev h1 and lorentz type l p q regularity properties for the obtained solutions the approach employed is unified for all dimensions n 1

on the schrodinger boussinesq system with singular initial data abstract we study the existence of local and global solutions for coupled schrodinger boussinesq systems with initial data in weak l r spaces these spaces contain singular functions with infinite l 2 mass such as homogeneous functions of negative degree moreover we analyze the self similarity and radial symmetry of solutions by considering initial data with the right homogeneity and radially symmetric respectively since functions in weak l r with r 2 have local finite l 2 mass the solutions obtained can be physically realized moreover for initial data in h s local solutions belong to h s which shows that the constructed data solution map in weak l r recovers h s regularity

a space time conditional intensity model for evaluating a wildfire hazard index numerical indices are commonly used as tools to aid wildfire management and hazard assessment although the use of such indices is widespread assessment of these indices in their respective regions of application is rare we evaluate the effectiveness of the burning index bi for predicting wildfire occurrences in los angeles county california using space time point process models these models are based on an additive decomposition of the conditional intensity with separate terms used to describe spatial and seasonal variability as well as contributions from the bi we fit the models to wildfire and bi data from the years 1976 2000 using a combination of nonparametric kernel smoothing methods and parametric maximum likelihood in addition to using the akaike information criterion aic to compare competing models we use new multidimensional residual methods based on approximate random thinning and rescaling to detect departures from the models and to ascertain the precise contribution of the bi to p

point processes and queues martingale dynamics i martingales 1 histories and stopping times 2 martingales 3 predictability 4 square integrable martingales references solutions to exercises chapter i ii point processes queues and intensities 1 counting processes and queues 2 watanabe s characterization 3 stochastic intensity general case 4 predictable intensities 5 representation of queues 6 random changes of time 7 cryptographic point processes references solutions to exercises chapter ii iii integral representation of point process martingales 1 the structure of internal histories 2 regenerative form of the intensity 3 the representation theorem 4 hilbert space theory of poissonian martingales 5 useful extensions references solutions to exercises chapter iii iv filtering 1 the theory of innovations 2 state estimates for queues and markov chains 3 continuous states and nontrivial prehistory references solutions to exercises chapter iv v flows in markovian networks of queues 1 single station the historical results and the filtering method 2 jackson s networks 3 burke s output theorem for networks 4 cascades and loops in jackson s networks 5 independence and poissonian flows in markov chains references solutions to exercises chapter v vi likelihood ratios 1 radon nikodym derivatives and tests of hypotheses 2 changes of intensities a la girsanov 3 filtering by the method of the probability of reference 4 applications 5 the capacity of a point process channel 6 detection formula187 references189 solutions to exercises chapter vi vii optimal control 1 modeling intensity controls 2 dynamic programming for intensity controls complete observation case 3 input regulation a case study in impulsive control 4 attraction controls 5 existence via likelihood ratio references solutions to exercises chapter vii viii marked point processes 1 counting measure and intensity kernels 2 martingale representation and filtering 3 radon nikodym derivatives 4 towards a general theory of intensity references solutions to exercises chapter viii a1 background in probability and stochastic processes 1 introduction 2 monotone class theorem 3 random variables 4 expectations 5 conditioning and independence 6 convergence 7 stochastic processes 8 markov processes references a2 stopping times and point process histories 1 stopping times 2 changes of time and meyer dellacherie s integration formula 3 point process histories references a3 wiener driven dynamical systems 1 ito s stochastic integral 2 square integrable brownian martingales 3 girsanov s theorem references a4 stieltjes lebesgue calculus 1 the stieltjes lebesgue integral 2 the product and exponential formulas references general bibliography

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved