Journal•ISSN: 0001-8678
Advances in Applied Probability
Cambridge University Press
About: Advances in Applied Probability is an academic journal published by Cambridge University Press. The journal publishes majorly in the area(s): Markov chain & Markov process. It has an ISSN identifier of 0001-8678. Over the lifetime, 3455 publications have been published receiving 97579 citations. The journal is also known as: Adv. appl. prob. & AAP.
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TL;DR: A coding theorem and weak converse are proved and a necessary and sufficient condition for a positive capacity is derived and upper and lower bounds on the capacity are obtained, which coincide for channels with symmetric structure.
Abstract: Summary The problem of transmitting information in a specified direction over a communication channel with three terminals is considered. Examples are given of the various ways of sending information. Basic inequalities for average mutual information rates are obtained. A coding theorem and weak converse are proved and a necessary and sufficient condition for a positive capacity is derived. Upper and lower bounds on the capacity are obtained, which coincide for channels with symmetric structure.
1,727 citations
TL;DR: The intrinsic random functions (IRF) are a particular case of the Guelfand generalized processes with stationary increments and constitute a much wider class than the stationary RF, and are used in practical applications for representing nonstationary phenomena as discussed by the authors.
Abstract: The intrinsic random functions (IRF) are a particular case of the Guelfand generalized processes with stationary increments. They constitute a much wider class than the stationary RF, and are used in practical applications for representing non-stationary phenomena. The most important topics are: existence of a generalized covariance (GC) for which statistical inference is possible from a unique realization; theory of the best linear intrinsic estimator (BLIE) used for contouring and estimating problems; the turning bands method for simulating IRF; and the models with polynomial GC, for which statistical inference may be performed by automatic procedures.
1,390 citations
TL;DR: In this paper, the authors developed criteria for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator, and applied the criteria to several specific processes, including linear stochastic systems under nonlinear feedback, work-modulated queues, general release storage processes and risk processes.
Abstract: In Part I we developed stability concepts for discrete chains, together with Foster–Lyapunov criteria for them to hold. Part II was devoted to developing related stability concepts for continuous-time processes. In this paper we develop criteria for these forms of stability for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator. Such test function criteria are found for non-explosivity, non-evanescence, Harris recurrence, and positive Harris recurrence. These results are proved by systematic application of Dynkin's formula. We also strengthen known ergodic theorems, and especially exponential ergodic results, for continuous-time processes. In particular we are able to show that the test function approach provides a criterion for f-norm convergence, and bounding constants for such convergence in the exponential ergodic case. We apply the criteria to several specific processes, including linear stochastic systems under non-linear feedback, work-modulated queues, general release storage processes and risk processes.
1,000 citations
TL;DR: In this article, a uniform asymptotic series for the probability distribution of the sum of a large number of independent random variables is derived, which is based on the fact that the major components of the distribution are determined by a saddle point and a singularity.
Abstract: In the present paper a uniform asymptotic series is derived for the probability distribution of the sum of a large number of independent random variables. In contrast to the usual Edgeworth-type series, the uniform series gives good accuracy throughout its entire domain. Our derivation uses the fact that the major components of the distribution are determined by a saddle point and a singularity at the origin. The analogous series for the probability density, due to Daniels, depends only on the saddle point. Two illustrative examples are presented that show excellent agreement with the exact distributions.
696 citations
TL;DR: This paper constructs index policies that depend on the rewards from each arm only through their sample mean, and achieves a O(log n) regret with a constant that is based on the Kullback–Leibler number.
Abstract: We consider a non-Bayesian infinite horizon version of the multi-armed bandit problem with the objective of designing simple policies whose regret increases sldwly with time. In their seminal work on this problem, Lai and Robbins had obtained a O(logn) lower bound on the regret with a constant that depends on the KullbackLeibler number. They also constructed policies for some specific families of probability distributions (including exponential families) that achieved the lower bound. In this paper we construct index policies that depend on the rewards from each arm only through their sample mean. These policies are computationally much simpler and are also applicable much more generally. They achieve a O(logn) regret with a constant that is also based on the Kullback-Leibler number. This constant turns out to be optimal for one-parameter exponential families; however, in general it is derived from the optimal one via a 'contraction' principle. Our results rely entirely on a few key lemmas from the theory of large deviations.
660 citations