the estimation of the model order in exponential families estimators are sought that achieve high exponential rate of decrease in the underestimation probability while keeping the overestimation probability exponent at a certain prescribed level it is assumed that a given integer is known to upper bound the true order some examples are given of possible applications of the proposed method in specific order estimation and hypothesis testing problems

a fitting algorithm for markov modulated poisson processes having two arrival rates abstract point processes with fluctuating arrival rates arise in many current applications of queueing theory notably in communications modeling markov modulated poisson processes mmpp have been used to describe such processes because they incorporate a mechanism to account for the temporal inhomogeneity of the arrival rates yet yield analytically tractable queueing results an iterative statistical procedure is developed for fitting mmpp having two arrival rates to observational data the procedure is largely numerical experimental and is motivated by maximum likelihood estimation

diffusion in a potential with a time dependent discontinuity we investigate the one dimensional diffusion of a particle in a v shaped potential combined with a time dependent jump at the tip employing the matching conditions we calculate the exact green function of the corresponding smoluchowski equation we then specialize the analysis to a harmonically oscillating height of the potential discontinuity we calculate the particle s mean position as a function of time and study its nonlinear features our analysis reveals a new type of stochastic resonance namely the time asymptotic amplitude of the mean position oscillations exhibits a maximum at an optimal value of the v potential slope

arbitrarily varying channels with constrained inputs and states random coding theorems are proved for discrete memoryless arbitrarily varying channels avcs with constraints on the transmitted codewords and channel state sequences two types of constraints are considered peak i e required for each n length sequence almost surely and average over the message set or over an ensemble for peak constraints on the codewords and on the channel state sequences the avc is shown to have a strong random coding capacity if the codewords and or the channel state sequences are constrained in the average sense the avcs do not possess strong capacities only epsilon capacities are shown to exist

income dynamics with a stationary double pareto distribution once controlled for the trend the distribution of personal income appears to be double pareto a distribution that obeys the power law exactly in both the upper and the lower tails i propose a model of income dynamics with a stationary distribution that is consistent with this fact using us male wage data for 1970 1993 i estimate the power law exponent in two ways i from each cross section assuming that the distribution has converged to the stationary distribution and ii from a panel directly estimating the parameters of the income dynamics model and obtain the same value of 8 4

asymptotically optimal classification for multiple tests with empirically observed statistics the decision problem of testing m hypotheses when the source is kth order markov and there are m or fewer training sequences of length n and a single test sequence of length n is considered k m n n are all given it is shown what the requirements are on m n n to achieve vanishing exponential error probabilities and how to determine or bound the exponent a likelihood ratio test that is allowed to produce a no match decision is shown to provide asymptotically optimal error probabilities and minimum no match decisions as an important serial case the binary hypotheses problem without rejection is discussed it is shown that for this configuration only one training sequence is needed to achieve an asymptotically optimal test

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

one dimensional diffusion through single and double square barriers exact solutions are obtained for the diffusion through single and double square potentials by using the laplace transform method we compare transmission of a classical particle through one barrier of given length and through two barriers with a well between them of the same overall length the influence of the barriers heights and widths as well as of the distances to the reflecting walls is studied in detail the results obtained are used to estimate the limits of applicability of the kramers rate theory

discrete time expectation maximization algorithms for markov modulated poisson processes in this paper we consider parameter estimation markov modulated poisson processes via robust filtering and smoothing techniques using the expectation maximization algorithm framework our filters and smoothers can be applied to estimate the parameters of our model in either an online configuration or an offline configuration further our estimator dynamics do not involve stochastic integrals and our new formulas in terms of time integrals are easily discretized and are written in numerically stable forms in w p malcolm r j elliott and j van der hoek ldquoon the numerical stability of time discretized state estimation via clark transformations rdquo presented at the ieee conf decision control mauii hi dec 2003

universal classification for hidden markov models binary hypotheses testing using empirically observed statistics is studied in the neyman pearson formulation for the hidden markov model hmm an asymptotically optimal decision rule is proposed and compared to the generalized likelihood ratio test glrt which has been shown in earlier studies to be asymptotically optimal for simpler parametric families the proof of the main theorem is provided the result can be applied to several types of hmms commonly used in speech recognition and communication applications several applications are demonstrated

on the emergence of a power law in the distribution of covid 19 cases the first confirmed case of coronavirus disease 2019 covid 19 in the us was reported on january 21 2020 by the end of march 2020 there were more than 180 000 confirmed cases in the us distributed across more than 2000 counties we find that the right tail of this distribution exhibits a power law with pareto exponent close to one we investigate whether a simple model of the growth of covid 19 cases involving gibrat s law can explain the emergence of this power law the model is calibrated to match i the growth rates of confirmed cases and ii the varying lengths of time during which covid 19 had been present within each county thus calibrated the model generates a power law with pareto exponent nearly exactly equal to the exponent estimated directly from the distribution of confirmed cases across counties at the end of march

diffusion process with two reflecting barriers in a time dependent potential we consider a brownian particle which is driven by a harmonically oscillating force the motion of which is restricted by two reflecting boundaries we solve the fokker planck equation using the finite element method and focus on the dynamics of the mean position of the particle in the time asymptotic regime as a function of the strength of the external force the response of the system i e the amplitude of the mean position and the dynamical shift in the stationary limit shows a resonancelike behavior as a function of the diffusion coefficient for certain parameter regimes we explain these numerical results heuristically and give some qualitative estimates

on classification with empirically observed statistics and universal data compression classification with empirically observed statistics is studied for finite alphabet sources efficient universal discriminant functions are described and shown to be related to universal data compression it is demonstrated that if one of the probability measure of the two classes is not known it is still possible to define a universal discrimination function which performs as the optimal likelihood ratio discriminant function which can be evaluated only if the probability measures of the two classes are available if both of the probability measures are not available but training vectors from at least one of the two classes are available it is demonstrated that no discriminant function can perform efficiency of the length of the training vectors does not grow at least linearly with the length of the classified vector a universal discriminant function is introduced and shown to perform efficiently when the length of the training vectors grows linearly with the length of the classified sequence in the sense that it yields an error exponent that is arbitrarily close to that of the optimal discriminant function

recursive estimation in mixture models with markov regime a recursive algorithm is proposed for estimation of parameters in mixture models where the observations are governed by a hidden markov chain the often badly conditioned information matrix is estimated and its inverse is incorporated into the algorithm the performance of the algorithm is studied by simulations of a symmetric normal mixture the algorithm seems to be stable and produce approximately normally distributed estimates provided the adaptive matrix is kept well conditioned some numerical examples are included

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

fuzzy control systems design and analysis a linear matrix inequality approach k tanaka h o wang eds john wiley sons inc 2001 320pp isbn 0 471 32324 1

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

recursive estimation of parameters in markov modulated poisson processes a hidden markov regime is a markov process that governs the time or space dependent distributions of an observed stochastic process recursive algorithms can be used to estimate parameters in mixed distributions governed by a markov regime the authors derive a recursive algorithm for estimation of parameters in a markov modulated poisson process also called a cox point process by this the authors mean a doubly stochastic poisson process with a time dependent intensity that can take on a finite number of different values the intensity switches randomly between the possible values according to a markov process the authors consider two different ways to observe the markov modulated poisson process in the first model the observations consist of the observed time intervals between events and in the second model they use the total number of events in successive intervals of fixed length they derive an algorithm for recursive estimation of the poisson intensities and the switch intensities between the two states and illustrate the algorithm in a simulation study the estimates of the switch intensities are based on the observed conditional switch probabilities

output stabilization of takagi sugeno fuzzy systems abstract in this paper the output stabilization problem of takagi sugeno fuzzy models is considered first a natural form of observers for such models is given sufficient conditions for their asymptotic convergence are given which are dual to those for the stability of state feedback fuzzy controllers we then show that a state feedback controller and an observer always yield a stabilizing output feedback controller provided that the stabilizing property of the control and the asymptotic convergence of the observer are guaranteed by the lyapunov method using positive definite matrices in this sense it is shown that the separation principle holds for takagi sugeno fuzzy systems two design examples are given to illustrate the theory

from entropy maximization to equality maximization gauss laplace pareto and subbotin abstract the entropy maximization paradigm of statistical physics is well known to generate the omnipresent gauss law in this paper we establish an analogous socioeconomic model which maximizes social equality rather than physical disorder in the context of the distributions of income and wealth in human societies we show that on a logarithmic scale the laplace law is the socioeconomic equality maximizing counterpart of the physical entropy maximizing gauss law and that this law manifests an optimized balance between two opposing forces i the rich and powerful striving to amass ever more wealth and thus to increase social inequality and ii the masses struggling to form more egalitarian societies and thus to increase social equality our results lead from log gauss statistics to log laplace statistics yield paretian power law tails of income and wealth distributions and show how the emergence of a middle class depends on the underlying levels of socioeconomic inequality and variability also in the context of asset prices with laplace distributed returns our results imply that financial markets generate an optimized balance between risk and predictability