the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

rbf methods in a stochastic volatility framework for greeks computation abstract in this paper we aim to apply a new proposed meshless approach for heston pde resolution in mathematical finance most classical models may be reformulated as partial differential equations pde which are commonly solved by finite difference and monte carlo methods alternatively bio inspired methods may be considered to select parameters and to solve said pdes in particular we focus on heston model pde and we solve it via radial basis functions rbf methods moreover some considerations on the computation of model parameters through learning approaches have been discussed we aim to price a vanilla call option focusing on the derivation of the formulae for its greeks profiles eventually we conclude rbfs are an accurate alternative method to price derivatives in a stochastic volatility framework especially since they allow for a fast and precise computation of greeks

schrodinger poisson equations without ambrosetti rabinowitz condition abstract we prove the existence of ground state solutions for a stationary schrodinger poisson equation in r 3 the proof is based on the mountain pass theorem and it does not require the ambrosetti rabinowitz condition

convexity of level sets of minimal graph on space form with nonnegative curvature abstract for the minimal graph defined on a convex ring in the space form with nonnegative curvature we obtain the regularity and the strict convexity about its level sets by the continuity method

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

least energy radial sign changing solution for the schrodinger poisson system in r3 under an asymptotically cubic nonlinearity abstract in this paper we consider the following schrodinger poisson system in the whole r 3 u u u f u in r 3 u 2 in r 3 where 0 and the nonlinearity f is asymptotically cubic at infinity this implies that the nonlocal term u and the nonlinear term f u are in some sense in a strict competition we show that the system admits a least energy sign changing and radial solution obtained by minimizing the energy functional on the so called nodal nehari set

a microscopic convexity principle for nonlinear partial differential equations we study microscopic convexity property of fully nonlinear elliptic and parabolic partial differential equations under certain general structure condition we establish that the rank of hessian 2u is of constant rank for any convex solution u of equation f 2u u u x 0 the similar result is also proved for parabolic equations some of geometric applications are also discussed

asymptotically min max bias robust m estimates of scale for positive random variables abstract asymptotically min max bias robust m estimates of scale are obtained for positive random variables with e contaminated distributions using any one of a broad class of loss functions of positive and negative bias any such estimate is a scaled order statistic with the order statistic and scaling constant determined by e the nominal distribution and the loss function some calculations for specific cases show that for a large range of e the min max order statistic solution has a breakdown point near 5 and is well approximated by a scaled median some calculations and monte carlo results indicate that the asymptotic result has considerable finite sample size relevance by virtue of the squared bias being at least as large as the variance for rather modest sample sizes depending on e and by virtue of attractive mean squared error performance in the presence of even rather small fractions of contamination

the role of the green s function in a non linear elliptic equation involving the critical sobolev exponent this paper is concerned with non linear elliptic problems of the type pe u u n 2 n 2 eu u 0 on u 0 on where is a smooth and bounded domain in rn n 4 and e 0 we show that if the ue are solutions of pe which concentrate around a point as e 0 then this point cannot be on the boundary of and is a critical point of the regular part of the green s function conversely we show that for n 5 and any non degenerate critical point x0 of the regular part of the green s function there exist solutions of pe concentrating around x0 as e 0

existence and convexity of local solutions to degenerate hessian equations abstract in this work we prove the existence of convex solutions to the following k hessian equation s k u k y g y u d u in the neighborhood of a point y 0 u 0 p 0 r n r r n where g c g y 0 u 0 p 0 0 k c is nonnegative near y 0 k y 0 0 and rank d y 2 k y 0 n k 1

multiplicity of normalized solutions for a class of nonlinear schrodinger poisson slater equations abstract in this paper we prove a multiplicity result of solutions for the following stationary schrodinger poisson slater equations 0 1 u u x 1 u 2 u u p 2 u 0 in r 3 where r is an undetermined parameter and p 10 3 6 we obtain couple solutions u with u having a prescribed l 2 norm our proofs are mainly inspired by a recent work of bartsch and de valeriola 7

positive solutions for a nonlocal schrodinger newton system involving critical nonlinearity abstract in this paper we study the critical schrodinger newton system with a nonlocal term and establish the existence of multiple positive solutions via using variational method

dynamic rating curve assessment in unstable rivers using ornstein uhlenbeck processes 1 the procedure of fitting rating curves in channels where the stage discharge relationship is subject to changes driven by morphological processes remains one of the major unsolved problems in hydrometry this paper addresses this issue by formulating the stage discharge relationship as a steady flow one segmented power law model with parameters that are viewed as stochastic processes with characteristics associated with the temporal instabilities of the channel elements governing the stage discharge relationship a bayesian analysis with informative priors and time stage discharge measurements as forcing data is used to determine the most plausible model and its posterior parameter distributions using markov chain monte carlo simulation techniques and particle filtering the proposed framework is applied to data from gauging stations in two unstable rivers and one stable river in norway

multiple positive solutions for a schrodinger poisson slater system abstract in this paper we investigate the existence of positive solutions to the following schrodinger poisson slater system u u u u p 2 u in u 2 in u 0 on where is a bounded domain in r 3 is a fixed positive parameter and p 2 2 n n 2 we prove that if p is near the critical sobolev exponent 2 then the number of positive solutions is greater then the lusternik schnirelmann category of

randomized shortest path problems two related models this letter addresses the problem of designing the transition probabilities of a finite markov chain the policy in order to minimize the expected cost for reaching a destination node from a source node while maintaining a fixed level of entropy spread throughout the network the exploration it is motivated by the following scenario suppose you have to route agents through a network in some optimal way for instance by minimizing the total travel cost nothing particular up to now you could use a standard shortest path algorithm suppose however that you want to avoid pure deterministic routing policies in order for instance to allow some continual exploration of the network avoid congestion or avoid complete predictability of your routing strategy in other words you want to introduce some randomness or unpredictability in the routing policy i e the routing policy is randomized this problem which will be called the randomized shortest path problem rsp is investigated in this work the global level of randomness of the routing policy is quantified by the expected shannon entropy spread throughout the network and is provided a priori by the designer then necessary conditions to compute the optimal randomized policy minimizing the expected routing cost are derived iterating these necessary conditions reminiscent of bellman s value iteration equations allows computing an optimal policy that is a set of transition probabilities in each node interestingly and surprisingly enough this first model while formulated in a totally different framework is equivalent to akamatsu s model 1996 appearing in transportation science for a special choice of the entropy constraint we therefore revisit akamatsu s model by recasting it into a sum over paths statistical physics formalism allowing easy derivation of all the quantities of interest in an elegant unified way for instance it is shown that the unique optimal policy can be obtained by solving a simple linear system of equations this second model is therefore more convincing because of its computational efficiency and soundness finally simulation results obtained on simple illustrative examples show that the models behave as expected

a proof of convergence for ant algorithms a proof of convergence for ant algorithms is developed ant algorithms were modeled as branching random processes the branching random walk and branching wiener process to derive rates of birth and death of ant paths substitution is then carried out in birth death processes which proves that a stable distribution is surely reached this indicates that ant algorithms converge with probability one this analogy models ant algorithms complexity parameters such as the number of cycles the degrees of freedom of problem and the number of ants

edge detection in noisy data using finite mixture distribution analysis abstract an algorithm which identifies discontinuities in noisy data is presented the signal is modelled as step edges with additive normally distributed noise present using finite mixture analysis and information criteria a variable number of mixtures are identified together with the location of the respective edges separating them the problem is solved using a dynamic programming approach which ensures globally optimal edge positions according to the signal model of a finite mixture of normal distributions the computational complexity is of order mn 2 where m is the number of discontinuities in the mixture and n is the number of data points in the signal the algorithm is tested on a range of real and synthetic signals and yields as accurate edge positions as a corresponding minimum square error method among applications for this algorithm is edge detection in medical images and examples from ultrasound imaging are included

an introduction to stochastic modeling stochastic modeling probability review the major discrete distributions rtant continuous distributions some elementary exercises useful functions integrals and sums conditional probability and conditional expectation the discrete case the dice game craps random sums conditioning on a continuous random variable markov chains introduction definitions transition probability matrices of a markov chain some markov chain models first step analysis some special markov chains functionals of random walks and success runs another look at first step analysis the long run behavior of markov chains regular transition probability matrices examples the classification of states the basic limit theorem of markov chains reducible markov chains sequential decisions and markov chains poisson processes the poisson distribution and the poisson processes the law of rare events distributions associated with the poisson process the uniform distribution and poisson processes spatial poisson processes compound and marked poisson processes continuous time markov chains pure birth processes ptire death processes birth and death processes the limiting behavior of birth and death processes birth and death processes with absorbing states finite state continuous time markov chains set valued processes renewal phenomena definition of a renewal process and related concepts some examples of renewal processes the poisson process viewed as a renewal process the asymptotic 3ehavior as renewal process

numerical determination of hitting time distributions from their laplace transforms one dimensional diffusions abstract in a previous paper we studied a method to determine the probability density of barrier crossing times by a brownian motion from the knowledge of its laplace transform this knowledge combined with the method of maximum entropy yields quite good reconstructions the aim of this work is to extend the previous analysis in two directions on one hand we consider diffusions with non constant coefficients this forces us to determine the laplace transform numerically or by means of simulations on the other hand and this is the gist of this note as numerical problems involve errors we consider as well two possible extensions of the maximum entropy procedure which allow us to incorporate those errors into the probability reconstruction process

catch estimation in the presence of declining catch rate due to gear saturation summary one strategy for estimating total catch is to employ two separate surveys that independently estimate total fishing effort and catch rate with the estimator for total catch formed by their product survey designs for estimating catch rate often involve interviewing the fishermen during their fishing episodes such roving designs result in incomplete episode data and characteristically have employed a model in which the catch rate is assumed to be constant over time this article extends the problem to that of estimating total catch in the presence of a declining catch rate due e g to gear saturation using a gill net fishery as an example a mean of ratios type of estimator for the catch rate together with its variance estimator are developed their performance is examined using simulations with special attention given to effects of restrictions on the roving survey window finally data from a fraser river gill net fishery are used to illustrate the use of the proposed estimator and to compare results with those from an estimator based on a constant catch rate

convexity of solutions of semilinear elliptic equations on considere le probleme elliptique suivant u f u dans u m sur ou est un domaine convexe de r 2 et m est soit une constante reelle soit on etablit que pour une bonne fonction monotone g t pout toute solution u on a g u est strictement convexe dans

preferential attachment in sexual networks many social networks are characterized by a highly uneven distribution of links the observed skewed distributions have in several cases been attributed to preferential attachment pa a tendency among nodes in a growing network to form new links preferentially to nodes with high numbers of links we test the pa conjecture in sexual contact networks a maximum likelihood estimation based expectation maximization fitting technique is used to model new partners over a 1 year period based on the number of partners in foregoing periods of 2 years 4 years and lifetime the pa model is modified to account for individual heterogeneity in the inclination to find new partners and fitted to norwegian survey data on heterosexual men and women results show evidence of nonrandom sublinear pa when comparing the growth in 3 to 5 year periods the potential implications of these findings are discussed

number and profile of low energy solutions for singularly perturbed klein gordon maxwell systems on a riemannian manifold abstract given a 3 dimensional riemannian manifold m g we investigate the existence of positive solutions of the klein gordon maxwell system e 2 g u a u u p 1 2 q v 1 2 u in m g v 1 q 2 u 2 v q u 2 in m and schrodinger maxwell system e 2 g u u u v u p 1 in m g v v q u 2 in m when p 4 6 we prove that the number of one peak solutions depends on the topological properties of the manifold m by means of the lusternik schnirelmann category

closed weingarten hypersurfaces in semi riemannian manifolds the existence of closed hypersurfaces of prescribed curvature in semi riemannian manifolds is proved provided there are barriers

projection functions area measures and the alesker fourier transform abstract dual to koldobsky s notion of j intersection bodies the class of j projection bodies is introduced generalizing minkowski s classical notion of projection bodies of convex bodies a fourier analytic characterization of j projection bodies in terms of their area measures of order j is obtained in turn this yields an equivalent characterization of j projection bodies involving alesker s fourier type transform on translation invariant smooth spherical valuations as applications of these results several basic properties of j projection bodies are established and new non trivial examples are constructed

regime switching volatility calibration by the baum welch method regime switching volatility models provide a tractable method of modelling stochastic volatility currently the most popular method of regime switching calibration is the hamilton filter we propose using the baum welch algorithm an established technique from engineering to calibrate regime switching models instead we demonstrate the baum welch algorithm and discuss the significant advantages that it provides compared to the hamilton filter we provide computational results of calibrating and comparing the performance of the baum welch and the hamilton filter to s p 500 and nikkei 225 data examining their performance in and out of sample

a generalized theory of preferential linking abstract there are diverse mechanisms driving the evolution of social networks a key open question dealing with understanding their evolution is how do various preferential linking mechanisms produce networks with different features in this paper we first empirically study preferential linking phenomena in an evolving online social network find and validate the linear preference we propose an analyzable model which captures the real growth process of the network and reveals the underlying mechanism dominating its evolution furthermore based on preferential linking we propose a generalized model reproducing the evolution of online social networks and present unified analytical results describing network characteristics for 27 preference scenarios we study the mathematical structure of degree distributions and find that within the framework of preferential linking analytical degree distributions can only be the combinations of finite kinds of functions which are related to rational logarithmic and inverse tangent functions and extremely complex network structure will emerge even for very simple sublinear preferential linking this work not only provides a verifiable origin for the emergence of various network characteristics in social networks but bridges the micro individuals behaviors and the global organization of social networks

tensor product markov chains abstract we analyze families of markov chains that arise from decomposing tensor products of irreducible representations this illuminates the burnside brauer theorem for building irreducible representations the mckay correspondence and pitman s 2 m x theorem the chains are explicitly diagonalizable and we use the eigenvalues eigenvectors to give sharp rates of convergence for the associated random walks for modular representations the chains are not reversible and the analytical details are surprisingly intricate in the quantum group case the chains fail to be diagonalizable but a novel analysis using generalized eigenvectors proves successful

on a system involving a critically growing nonlinearity abstract this paper deals with the system u u q u 3 u in b r q u 5 in b r u 0 on b r we prove existence and nonexistence results depending on the value of

existence of positive solutions to the schrodinger poisson system without compactness conditions abstract in this paper we discuss the existence of a positive radial solution to a generalized schrodinger poisson system without compactness conditions by the method of the combination of a cut off function a monotonicity trick and a pohozaev type identity we obtain the boundedness of a palais smale sequence

analytic treatment of consensus achievement in the single type zealotry voter model abstract we introduce zealots of one opinion in the voter model on a complete graph and examine how they affect consensus achievement using first step analysis for markov chains to obtain an exact solution we find that the mean consensus time scales with the population size n increasing the number of zealots z will decrease the consensus time in a power law fashion for large z the mean magnetization was also analytically obtained and was found to contain an exponential dependence on z the dynamics for the complete graph are qualitatively similar to those obtained in another study for the barabasi albert network in general the existence of zealots serves to hasten consensus except in the case where only a few zealots oppose the vast majority

existence and nonexistence of positive solutions for a static schrodinger poisson slater equation abstract in this paper we study the following type of the schrodinger poisson slater equation with critical growth u u 2 1 4 x u u p 1 u u 4 u in r 3 where 0 and p 11 7 5 for the case of p 2 5 we develop a novel perturbation approach together with the well known mountion pass theorem to prove the existence of positive ground states for the case of p 2 we obtain the nonexistence of nontrivial solutions by restricting the range of and also study the existence of positive solutions by the constrained minimization method for the case of p 11 7 2 we use a truncation technique developed by brezis and oswald 9 together with a measure representation concentration compactness principle due to lions 27 to prove the existence of radial symmetrical positive solutions for 0 with some 0 the above results nontrivially extend some theorems on the subcritical case obtained by ianni and ruiz 18 to the critical case

probability of stochastic processes and spacetime geometry abstract we made a first attempt to associate a probabilistic description of stochastic processes like birth death processes with spacetime geometry in the schwarzschild metrics on distance scales from the macro to the micro domains we idealize an ergodic system in which system states communicate through a curved path composed of transition arrows where each arrow corresponds to a positive analogous birth or death rate

spectral theory of metastability and extinction in a branching annihilation reaction we apply the spectral method recently developed by the authors to calculate the statistics of a reaction limited multistep birth death process or chemical reaction that includes as elementary steps branching a 2a and annihilation 2a 0 the spectral method employs the generating function technique in conjunction with the sturm liouville theory of linear differential operators we focus on the limit when the branching rate is much higher than the annihilation rate and obtain accurate analytical results for the complete probability distribution including large deviations of the metastable long lived state and for the extinction time statistics the analytical results are in very good agreement with numerical calculations furthermore we use this example to settle the issue of the lacking boundary condition in the spectral formulation

filling of a poisson trap by a population of random intermittent searchers we extend the continuum theory of random intermittent search processes to the case of n independent searchers looking to deliver cargo to a single hidden target located somewhere on a semi infinite track each searcher randomly switches between a stationary state and either a leftward or rightward constant velocity state we assume that all of the particles start at one end of the track and realize sample trajectories independently generated from the same underlying stochastic process the hidden target is treated as a partially absorbing trap in which a particle can only detect the target and deliver its cargo if it is stationary and within range of the target the particle is removed from the system after delivering its cargo as a further generalization of previous models we assume that up to n successive particles can find the target and deliver its cargo assuming that the rate of target detection scales as 1 n we show that there exists a well defined mean field limit n rightarrow infty in which the stochastic model reduces to a deterministic system of linear reaction hyperbolic equations for the concentrations of particles in each of the internal states these equations decouple from the stochastic process associated with filling the target with cargo the latter can be modeled as a poisson process in which the time dependent rate of filling lambda t depends on the concentration of stationary particles within the target domain hence we refer to the target as a poisson trap we analyze the efficiency of filling the poisson trap with n particles in terms of the waiting time density f n t the latter is determined by the integrated poisson rate mu t int 0 t lambda s ds which in turn depends on the solution to the reaction hyperbolic equations we obtain an approximate solution for the particle concentrations by reducing the system of reaction hyperbolic equations to a scalar advection diffusion equation using a quasi steady state analysis we compare our analytical results for the mean field model with monte carlo simulations for finite n we thus determine how the mean first passage time mfpt for filling the target depends on n and n

positive solutions for double singularly perturbed schrodinger maxwell systems abstract we show that the number of solutions of a double singularly perturbed schrodinger maxwell system on a smooth bounded domain r 3 depends on the topological properties of the domain in particular if is non contractible we obtain cat 1 positive solutions the result is obtained via lusternik schnirelmann category theory

concentration and compactness in nonlinear schrodinger poisson system with a general nonlinearity in this paper we use a concentration and compactness argument to prove the existence of a nontrivial non radial solution to the nonlinear schrodinger poisson equations in r3 assuming on the nonlinearity the general hypotheses introduced by berestycki and lions

non linear shot noise levy noah joseph abstract we introduce and study a generic non linear shot noise system model shots of random magnitudes arrive to the system stochastically following an arbitrary time homogeneous poisson point process after hitting the system the magnitude of an arriving shot decays to zero the decay is governed by an arbitrary differential equation dynamics shots are independent and their overall effect on the system is additive the system s noise level at time t equals the sum of the magnitudes at time t of all the shots arriving to the system prior to time t the resulting shot noise is i a levy process when the decay dynamics are degenerate ii a levy driven ornstein uhlenbeck process when the decay dynamics are linear and iii a stationary non markov process when the decay dynamics are non linear the resulting shot noise admits an underlying levy structure which we explicitly compute and can yield both the noah effect and the joseph effect closed form analytic formulae for various statistics are derived including the log laplace transform and cumulants of the stationary noise level the process auto covariance function and the process range of dependence

a fourier transform approach to christoffel s problem we use fourier transform techniques to provide a new approach to berg s solution of the christoffel problem this leads to an explicit description of berg s spherical kernel and to new regularity properties of the associated integral transform

convergence of percolation probability functions to cumulative distribution functions on square lattices with 1 0 neighborhood abstract we consider a percolation model on square lattices with sites weighted by beta distributed random variables s beta a b with a positive real parameters a 0 and b 0 using the monte carlo method we estimate the percolation probability p as a relative frequency p averaged over the target subset of sites on a square lattice as a result of the comparative analysis we formulate two empirical hypotheses the first on the correspondence of percolation thresholds p c to p 0 quantiles where level p 0 0 592746 coincides with the percolation threshold for the site percolation model on a square lattice of random variables s i weighing sites of the square lattice and the second on the convergence of statistical estimates of percolation probability functions p p to cumulative distribution functions f s i p of these variables s i for the supercritical values of the occupation probability p p c

a hopf theorem for non constant mean curvature and a conjecture of a d alexandrov we prove a uniqueness theorem for immersed spheres of prescribed non constant mean curvature in homogeneous three manifolds in particular this uniqueness theorem proves a conjecture by a d alexandrov about immersed spheres of prescribed weingarten curvature in mathbb r 3 for the special but important case of prescribed mean curvature as a consequence we extend the classical hopf uniqueness theorem for constant mean curvature spheres to the case of immersed spheres of prescribed antipodally symmetric mean curvature in mathbb r 3

multiple solutions for schrodinger poisson type equation with magnetic field in this paper we consider the multiplicity and concentration behavior for a nonlinear schrodinger poisson type equation with magnetic field by penalization method and ljusternik schnirelmann theory we present the relationship between the number of solutions and the topology of the set where the potential attains its minimum value

estimation of current reliability in a duane based reliability growth model in this article i investigate the statistical inference concerning the current field stage reliability of a reliability growth model the model assuming a step intensity structure evolves from the physical consideration of the duane learning curve property and incorporates the effect of a testanalyze and fix program that is typically undertaken in a developmental testing program both exact and large sample distributional results are derived for the maximum likelihood and the least squares estimators of the current intensity under the assumption that the step intensity model represents the reality i provide an assessment of the extent of misspecification when the widely used power law process model is fit to the failure data of a system experiencing recurrent failures extensive simulation results are carried out to supplement the theoretical findings an illustration with a dataset is provided as a demonstration of the application of the inference results