on robust hurwitz polynomials in this note kharitonov s theorem on robust hurwitz polynomials is simplified for low order polynomials specifically for n 3 4 and 5 the number of polynomials required to check robust stability is one two and three respectively instead of four furthermore it is shown that for n geq 6 the number of polynomials for robust stability checking is necessarily four thus further simplification is not possible the same simplifications arise in robust schur polynomials by using the bilinear transformation applications of these simplifications to two dimensional polynomials as well as to robustness for single parameters are indicated

on the stability of low order perturbed polynomials it is shown that for low order perturbed continuous system polynomials n 6 stability can be guaranteed by checking very simple conditions based on the hermite biehler theorem this result is analogous to a recent result by anderson et al based on kharitonov s conditions

probabilities of concurrent extremes the statistical modelling of spatial extremes has recently made major advances much of its focus so far has been on the modelling of the magnitudes of extreme events but little attention has been paid on the timing of extremes to address this gap this paper introduces the notion of extremal concurrence suppose that one measures precipitation at several synoptic stations over multiple days we say that extremes are concurrent if the maximum precipitation over time at each station is achieved simultaneously e g on a single day under general conditions we show that the finite sample concurrence probability converges to an asymptotic quantity deemed extremal concurrence probability using palm calculus we establish general expressions for the extremal concurrence probability through the max stable process emerging in the limit of the componentwise maxima of the sample explicit forms of the extremal concurrence probabilities are obtained for various max stable models and several estimators are introduced in particular we prove that the pairwise extremal concurrence probability for max stable vectors is precisely equal to the kendall s tau the estimators are evaluated by using simulations and applied to study the concurrence patterns of temperature extremes in the united states the results demonstrate that concurrence probability can provide a powerful new perspective and tools for the analysis of the spatial structure and impact of extremes

stability of polynomials under coefficient perturbation let the real polynomial a 0 x n a 1 x n 1 a n 1 x a n be stable and let the real numbers b k c k geq 0 0 leq k leq n be given we present a simple determinant criterion for finding the largest t 0 geq 0 such that the polynomial alpha 0 x n alpha 1 x n 1 alpha n 1 x alpha n is stable for all alpha k in a k b k t 0 a k c k t 0 cup a k 0 leq k leq n several further observations allow us to reduce the computational cost considerably

modelling extreme multivariate events summary the classical treatment of multivariate extreme values is through componentwise ordering though in practice most interest is in actual extreme events here the point process of observations which are extreme in at least one component is considered parametric models for the dependence between components must satisfy certain constraints two new techniques for generating such models are presented aspects of the statistical estimation of the resulting models are discussed and are illustrated with an application to oceanographic data

wide sense stability of discrete and continuous time linear systems in the complex case canonical reflection coefficients are used to determine the number of roots appearing on the unit circle and their multiplicities for a stable polynomial with no zero outside the unit circle a criterion so that a stable polynomial has no multiple zeros on the unit circle is then deduced and transposed to the continuous time linear systems in the complex case

markov chain models for threshold exceedances in recent research on extreme value statistics there has been an extensive development of threshold methods first in the univariate case and subsequently in the multivariate case as well in this paper an alternative methodology for extreme values of univariate time series is developed by assuming that the time series is markovian and using bivariate extreme value theory to suggest appropriate models for the transition distributions a new likelihood representation for threshold methods is presented which we apply to a markovian time series an important motivation for developing this kind of theory is the possibility of calculating probability distributions for functionals of extreme events we address this issue by showing how a theory of compound poisson limits for additive functionals can be combined with simulation to obtain numerical solutions for problems of practical interest the methods are illustrated by application to temperature data

dependence modelling for spatial extremes current dependence models for spatial extremes are based upon max stable processes within this class there are few inferentially viable models available and we propose one further model more problematic are the restrictive assumptions that must be made when using max stable processes to model dependence for spatial extremes it must be assumed that the dependence structure of the observed extremes is compatible with a limiting model that holds for all events more extreme than those that have already occurred this problem has long been acknowledged in the context of finite dimensional multivariate extremes in particular when data display dependence at observable levels but are independent in the limit we propose a flexible class of models that is suitable for such data in a spatial context in addition we consider the situation where the extremal dependence structure may vary with distance we apply our models to spatially referenced significant wave height data from the north sea finding evidence that their extremal structure is not compatible with a limiting dependence model

conditional simulation of max stable processes summary since many environmental processes such as heat waves or precipitation are spatial in extent it is likely that a single extreme event affects several loca tions and the areal modelling of extremes is therefore essential if the spatial dependence of e xtremes has to be appropriately taken into account this paper proposes a framework for conditional simulations of max stable processes and give closed forms for brown resnick and schlather processes we test the method on simulated data and give an application to extreme rainfall around zurich and extreme temperature in switzerland results show that the proposed framework provides accurate conditional simulations and can handle real sized problems

on the strict and wide sense stability robustness of uncertain systems application of a new frequency criterion abstract in this paper we discuss a new frequency domain graphical approach for robust stability of uncertain systems this method is based on mikhailov s criterion and it requires the plotting of only one hodograph and evaluation of two boundary conditions moreover this approach is extended to a more general robust stability sense i e extended and wide sense hurwitz stability which may be applied to a number of robustness problems such as positivity nonnegativity spectral analysis and array processing

maximal unidirectional perturbation bounds for stability of polynomials and matrices abstract given a stable polynomial or matrix we consider a class of unidirectional perturbations in this note we provide a closed form for the maximal perturbation bounds under which stability is preserved the results are then used to derive a closed form for the maximal stability box around the coefficients of a nominally stable polynomial

stability of a hurwitz polynomial under coefficient perturbations necessary and sufficient conditions necessary and sufficient conditions for a perturbed polynomial to remain hurwitz are given the conditions allow considerable freedom in allocating different weights to various coefficients to reflect different levels of uncertainty in the coefficients the new conditions are an extension of a previous result of the author in which sufficient conditions for the same problem were obtained

queue aware distributive resource control for delay sensitive two hop mimo cooperative systems in this paper we consider a queue aware distributive resource control algorithm for two hop mimo cooperative systems we shall illustrate that relay buffering is an effective way to reduce the intrinsic half duplex penalty in cooperative systems the complex interactions of the queues at the source node and the relays are modeled as an average cost infinite horizon markov decision process mdp the traditional approach solving this mdp problem involves centralized control with huge complexity to obtain a distributive and low complexity solution we introduce a linear structure which approximates the value function of the associated bellman equation by the sum of per node value functions we derive a distributive two stage two winner auction based control policy which is a function of the local csi and local qsi only furthermore to estimate the best fit approximation parameter we propose a distributive online stochastic learning algorithm using stochastic approximation theory finally we establish technical conditions for almost sure convergence and show that under heavy traffic the proposed low complexity distributive control is global optimal

a new robust variable step size nlms algorithm a new framework for designing robust adaptive filters is introduced it is based on the optimization of a certain cost function subject to a time dependent constraint on the norm of the filter update particularly we present a robust variable step size nlms algorithm which optimizes the square of the a posteriori error we also show the link between the proposed algorithm and another one derived using a robust statistics approach in addition a theoretical model for predicting the transient and steady state behavior and a proof of almost sure filter convergence are provided the algorithm is then tested in different environments for system identification and acoustic echo cancelation applications

linear system stability under parameter uncertainties a sufficient condition for linear system stability under parameter variations is presented it yields parameter bounds which are not conservative and the test is easily implemented on a digital computer

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

an actor critic algorithm for constrained markov decision processes abstract an actor critic type reinforcement learning algorithm is proposed and analyzed for constrained controlled markov decision processes the analysis uses multiscale stochastic approximation theory and the envelope theorem of mathematical economics

strict hurwitz property of polynomials under coefficient perturbation a simple procedure for computing the allowable interval coefficient perturbations of a strictly stable polynomial is presented the amount of computations involved is very little while the procedure is able to handle the case where the relative uncertainty of the polynomial coefficients are not known it can also handle the case of linearly dependent parameter uncertainties the procedure can also be modified to treat the case of simple nonlinear dependent parameter uncertainties the details of the modified procedure will depend on the nature of the nonlinearity

on robust hurwitz and schur polynomials based on results of a v lipatov and n i sokolov 1979 simple sufficient conditions for the robust stability of both strictly hurwitz and schur interval polynomials are obtained furthermore sufficient conditions are derived for robustness of strictly hurwitz and schur polynomials whose coefficients of linear functions of a single parameter several examples are discussed illustrating the derived results

generalization of the hermite biehler theorem and applications a generalization of the hermite biehler theorem for the open left half plane is derived using this generalization a graphical method for checking the stability of linear uncertain continuous time systems is presented the stability regions belong to a class of simply connected regions that includes most of the regions of interest in control

the o d e method for convergence of stochastic approximation and reinforcement learning it is shown here that stability of the stochastic approximation algorithm is implied by the asymptotic stability of the origin for an associated ode this in turn implies convergence of the algorithm several specific classes of algorithms are considered as applications it is found that the results provide i a simpler derivation of known results for reinforcement learning algorithms ii a proof for the first time that a class of asynchronous stochastic approximation algorithms are convergent without using any a priori assumption of stability iii a proof for the first time that asynchronous adaptive critic and q learning algorithms are convergent for the average cost optimal control problem

modeling spatial processes with unknown extremal dependence class abstractmany environmental processes exhibit weakening spatial dependence as events become more extreme well known limiting models such as max stable or generalized pareto processes cannot capture this which can lead to a preference for models that exhibit a property known as asymptotic independence however weakening dependence does not automatically imply asymptotic independence and whether the process is truly asymptotically in dependent is usually far from clear the distinction is key as it can have a large impact upon extrapolation that is the estimated probabilities of events more extreme than those observed in this work we present a single spatial model that is able to capture both dependence classes in a parsimonious manner and with a smooth transition between the two cases the model covers a wide range of possibilities from asymptotic independence through to complete dependence and permits weakening dependence of extremes even under asymptotic dependence censored likelihood based

learning algorithms for markov decision processes with average cost this paper gives the first rigorous convergence analysis of analogues of watkins s q learning algorithm applied to average cost control of finite state markov chains we discuss two algorithms which may be viewed as stochastic approximation counterparts of two existing algorithms for recursively computing the value function of the average cost problem the traditional relative value iteration rvi algorithm and a recent algorithm of bertsekas based on the stochastic shortest path ssp formulation of the problem both synchronous and asynchronous implementations are considered and analyzed using the ode method this involves establishing asymptotic stability of associated ode limits the ssp algorithm also uses ideas from two time scale stochastic approximation

exploiting occurrence times in likelihood inference for componentwise maxima multivariate extreme value distributions arise as the limiting distributions of normalised componentwise maxima they are often used to model multivariate data that can be regarded as the componentwise maxima of some unobserved underlying multivariate process in many applications we have extra information we often know the locations of the maxima within the underlying process if the process is temporal this knowledge is frequently available through the dates on which the maxima are recorded we show how to incorporate this extra information into maximum likelihood procedures asymptotic and small sample efficiency results are presented for the dependence parameter in the logistic parametric sub class of bivariate extreme value distributions we conclude with an application to sea levels

asynchronous stochastic approximations the asymptotic behavior of a distributed asynchronous stochastic approximation scheme is analyzed in terms of a limiting nonautonomous differential equation the relation between the latter and the relative values of suitably rescaled relative frequencies of updates of different components is underscored

modelling multivariate extreme value distributions summary multivariate extreme value distributions arise as the limiting joint distribution of normalized componentwise maxima minima no parametric family exists for the depen dence between the margins this paper extends to more than two variables the models and results for the bivariate case obtained by tawn 1988 two new families of physically motivated parametric models for the dependence structure are presented and are illus trated with an application to trivariate extreme sea level data in the analysis of environmental extreme value data there is often need to study joint inter site extreme behaviour examples are joint flooding at various sea ports or at various rain gauges in this paper the class of multivariate extreme value distributions is considered the marginal distributions are all extreme value distributions without loss of generality we follow pickands s 1981 approach in transforming the margins to unit mean exponential distributions the resulting class of p variable multivariate exponential distributions satisfies a strong stability relation de haan resnick 1977 and pickands 1981 show that the resulting dependence structure is uniquely specified up to an arbitrary finite positive measure on p 1 variables therefore the bivariate dependence structure is univariate only when p 3 as considered here does the problem become really multivari ate in addition unlike in the multivariate normal distribution the multivariate depen dence structure is generally only restricted and not uniquely specified by the dependence structure of all possible pairs much has been written about the representations of multivariate extremes see resnick 1987 for a good review on the other hand models and estimation for such distributions have received little attention these aspects are considered here as no finite parametric family exists for the general dependence structure it must be modelled in some way thus true multivariate models are required using the most flexible bivariate model of tawn 1988 as a basis multivariate extensions are generated a model derived in the discrete choice literature will also be introduced and extended the resulting families of models are physically motivated flexible and possess hierarchical properties

composite likelihood estimation for the brown resnick process summary genton et al 2011 investigated the gain in efficiency when triplewise rather than pairwise likelihood is used to fit the popular smith max stable model for spatial extremes we generalize their results to the brown resnick model and show that the efficiency gain is substantial only for very smooth processes which are generally unrealistic in applications

likelihood based inference for max stable processes the last decade has seen max stable processes emerge as a common tool for the statistical modeling of spatial extremes however their application is complicated due to the unavailability of the multivariate density function and so likelihood based methods remain far from providing a complete and flexible framework for inference in this article we develop inferentially practical likelihood based methods for fitting max stable processes derived from a composite likelihood approach the procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost the utility of this methodology is examined via simulation and illustrated by the analysis of united states precipitation extremes

invariance of the strict hurwitz property for polynomials with perturbed coefficients given a strictly hurwitz polynomial f lambda lambda n a n 1 lambda n 1 a n 2 lambda n 2 a 1 lambda a 0 it is of interest to know how much the coefficients a i can be perturbed while simultaneously preserving the strict hurwitz property for systems with n leq 4 maximal intervals of the a i are given in a recent paper by guiver and bose 1 in this note a theorem of kharitonov is exploited to obtain a general result for polynomials of any degree

frequency domain criteria for l sup p robust stability of continuous linear systems necessary and sufficient criteria in the frequency domain for robust stability are given under the assumption that coefficients of a characteristic polynomial belong to a transformed l sup p ball three cases are considered in detail p infinity interval uncertainty p 2 ellipsoidal uncertainty and p 1 octahedral uncertainty it is shown that frequency domain stability criteria are efficient when one deals with robust stability problems the frequency domain approach considered can be extended to various problems of robust stability

a generalization of kharitonov s four polynomial concept for robust stability problems with linearly dependent coefficient perturbations kharitonov s four polynomial concept is generalized to the case of linearly dependent coefficient perturbations and more general zero location regions to this end a specially constructed scalar function of a scalar variable is instrumental to the robustness analysis the present work is motivated by two fundamental limitations of kharitonov s theorem namely 1 the theorem only applies to polynomials with independent coefficient perturbations and 2 it only applies to zeros in the left hand plane

geostatistics of extremes we describe a prototype approach to flexible modelling for maxima observed at sites in a spatial domain based on fitting of max stable processes derived from underlying gaussian random fields the models we propose have generalized extreme value marginal distributions throughout the spatial domain consistent with statistical theory for maxima in simpler cases and can incorporate both geostatistical correlation functions and random set components parameter estimation and fitting are performed through composite likelihood inference applied to observations from pairs of sites with occurrence times of maxima taken into account if desired and competing models are compared using appropriate information criteria diagnostics for lack of model fit are based on maxima from groups of sites the approach is illustrated using annual maximum temperatures in switzerland with risk analysis proposed using simulations from the fitted max stable model drawbacks and possible developments of the approach are discussed

some results on robust stability of discrete time systems the theorem of kharitonov on the hurwitz property of interval families of polynomials cannot be extended in genera to obtain sufficient conditions for the stability of families of characteristic polynomials of discrete time systems necessary and sufficient conditions for this stability problem are given such conditions naturally give rise to a computationally efficient stability test which requires the solution of a one parameter optimization problem and which can be considered as a counterpart to the kharitonov test for continuous time systems at the same time the method used to derive the stability conditions provides a procedure for solving another stability robustness problem i e the estimation of the largest domain of stability with a rectangular box shape around given nominal values of the polynomial coefficients

a conditional approach for multivariate extreme values with discussion summary multivariate extreme value theory and methods concern the characterization estimation and extrapolation of the joint tail of the distribution of a d dimensional random variable existing approaches are based on limiting arguments in which all components of the variable become large at the same rate this limit approach is inappropriate when the extreme values of all the variables are unlikely to occur together or when interest is in regions of the support of the joint distribution where only a subset of components is extreme in practice this restricts existing methods to applications where d is typically 2 or 3 under an assumption about the asymptotic form of the joint distribution of a d dimensional random variable conditional on its having an extreme component we develop an entirely new semiparametric approach which overcomes these existing restrictions and can be applied to problems of any dimension we demonstrate the performance of our approach and its advantages over existing methods by using theoretical examples and simulation studies the approach is used to analyse air pollution data and reveals complex extremal dependence behaviour that is consistent with scientific understanding of the process we find that the dependence structure exhibits marked seasonality with ex tremal dependence between some pollutants being significantly greater than the dependence at non extreme levels

stationary max stable fields associated to negative definite functions let wi i be independent copies of a zero mean gaussian process w t t d with stationary increments and variance 2 t independently of wi let i 1 ui be a poisson point process on the real line with intensity e y dy we show that the law of the random family of functions vi i where vi t ui wi t 2 t 2 is translation invariant in particular the process t i 1 vi t is a stationary max stable process with standard gumbel margins the process arises as a limit of a suitably normalized and rescaled pointwise maximum of n i i d stationary gaussian processes as n if and only if w is a nonisotropic fractional brownian motion on d under suitable conditions on w the process has a mixed moving maxima representation

estimation of husler reiss distributions and brown resnick processes summary estimation of extreme value parameters from observations in the max domain of attraction of a multivariate max stable distribution commonly uses aggregated data such as block maxima multivariate peaks over threshold methods in contrast exploit additional information from the non aggregated large observations we introduce an approach based on peaks over thresholds that provides several new estimators for processes in the max domain of attraction of the frequently used husler reiss model and its spatial extension brown resnick processes the method relies on increments t0 conditional on t0 exceeding a high threshold where t0 is a fixed location when the marginals are standardized to the gumbel distribution these increments asymptotically form a gaussian process resulting in computationally simple estimates of the husler reiss parameter matrix and particularly enables parametric inference for brown resnick processes based on high dimensional multivariate densities this is a major advantage over composite likelihood methods that are commonly used in spatial extreme value statistics since they rely only on bivariate densities a simulation study compares the performance of the new estimators with other commonly used methods as an application we fit a non isotropic brown resnick process to the extremes of 12 year data of daily wind speed measurements

efficient inference and simulation for elliptical pareto processes recent advances in extreme value theory have established ell pareto processes as the natural limits for extreme events defined in terms of exceedances of a risk functional here we provide methods for the practical modelling of data based on a tractable yet flexible dependence model we introduce the class of elliptical ell pareto processes which arise as the limit of threshold exceedances of certain elliptical processes characterized by a correlation function and a shape parameter an efficient inference method based on maximizing a full likelihood with partial censoring is developed novel procedures for exact conditional and unconditional simulation are proposed these ideas are illustrated using precipitation extremes in switzerland

efficient inference for spatial extreme value processes associated to log gaussian random functions max stable processes arise as the only possible nontrivial limits for maxima of affinely normalized identically distributed stochastic processes and thus form an important class of models for the extreme values of spatial processes until recently inference for max stable processes has been restricted to the use of pairwise composite likelihoods due to intractability of higher dimensional distributions in this work we consider random fields that are in the domain of attraction of a widely used class of max stable processes namely those constructed via manipulation of log gaussian random functions for this class we exploit limiting d dimensional multivariate poisson process intensities of the underlying process for inference on all d vectors exceeding a high marginal threshold in at least one component employing a censoring scheme to incorporate information below the marginal threshold we also consider the d dimensional distributions for the equivalent max stable process and perform full likelihood inference by exploiting the methods of stephenson tawn 2005 where information on the occurrence times of extreme events is shown to dramatically simplify the likelihood the stephenson tawn likelihood is in fact simply a special case of the censored poisson process likelihood we assess the improvements in inference from both methods over pairwise likelihood methodology by simulation

stochastic throughput optimization for two hop systems with finite relay buffers optimal queueing control of multihop networks remains a challenging problem even in the simplest scenarios in this paper we consider a two hop half duplex relaying system with random channel connectivity the relay is equipped with a finite buffer we focus on stochastic link selection and transmission rate control to maximize the average system throughput subject to a half duplex constraint we formulate this stochastic optimization problem as an infinite horizon average cost markov decision process mdp which is well known to be a difficult problem by using sample path analysis and exploiting the specific problem structure we first obtain an equivalent bellman equation with reduced state and action spaces by using relative value iteration algorithm we analyze the properties of the value function of the mdp then we show that the optimal policy has a threshold based structure by characterizing the supermodularity in the optimal control based on the threshold based structure and markov chain theory we further simplify the original complex stochastic optimization problem to a static optimization problem over a small discrete feasible set and propose a low complexity algorithm to solve the simplified static optimization problem by making use of its special structure furthermore we obtain the closed form optimal threshold for the symmetric case the analytical results obtained in this paper also provide design insights for two hop relaying systems with multiple relays equipped with finite relay buffers

frequency domain conditions for the stability of perturbed polynomials new necessary and sufficient conditions for the stability of perturbed polynomials of continuous systems are given in the frequency domain the conditions are equivalent and in some respects more powerful than the well known kharitonov conditions the new conditions allow considerable freedom in distributing the available uncertainty margin among the different coefficients of a polynomial and provide an indication as to whether the maximum allowable margin of uncertainty for a given polynomial has been reached

on the likelihood function of gaussian max stable processes summary wederiveaclosedformexpressionforthelikelihoodfunctionofagaussianmax stableprocessindexed by r d at p d 1 sites d 1 we demonstrate the gain in efficiency in the maximum composite likelihood estimators of the covariance matrix from p 2t op 3 sites in r 2 by means of a monte carlo