Journal•ISSN: 1050-5164
Annals of Applied Probability
Institute of Mathematical Statistics
About: Annals of Applied Probability is an academic journal published by Institute of Mathematical Statistics. The journal publishes majorly in the area(s): Markov chain & Random walk. It has an ISSN identifier of 1050-5164. Over the lifetime, 2188 publications have been published receiving 105020 citations. The journal is also known as: The annals of applied probability.
Topics: Markov chain, Random walk, Stochastic differential equation, Central limit theorem, Population
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the authors consider scaling the proposal distribution of a multidimensional random walk Metropolis algorithm in order to maximize the efficiency of the algorithm and obtain a weak convergence result as the dimension of a sequence of target densities, n, converges to $\infty$.
Abstract: This paper considers the problem of scaling the proposal distribution of a multidimensional random walk Metropolis algorithm in order to maximize the efficiency of the algorithm. The main result is a weak convergence result as the dimension of a sequence of target densities, n, converges to $\infty$. When the proposal variance is appropriately scaled according to n, the sequence of stochastic processes formed by the first component of each Markov chain converges to the appropriate limiting Langevin diffusion process. The limiting diffusion approximation admits a straightforward efficiency maximization problem, and the resulting asymptotically optimal policy is related to the asymptotic acceptance rate of proposed moves for the algorithm. The asymptotically optimal acceptance rate is 0.234 under quite general conditions. The main result is proved in the case where the target density has a symmetric product form. Extensions of the result are discussed.
1,807 citations
TL;DR: Regular affine processes as discussed by the authors unify the concepts of continuous state branching processes with immigration and Ornstein-Uhlenbeck type processes, and provide foundations for a wide range of financial applications.
Abstract: We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration and Ornstein-Uhlenbeck type processes. We show, and provide foundations for, a wide range of financial applications for regular affine processes.
1,082 citations
TL;DR: In this article, the authors studied the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market and showed that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less then one.
Abstract: The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less then one. (author's abstract)
1,071 citations
TL;DR: In this article, the second largest eigenvalue and spectral gap of a reversible Markov chain were derived for the random walk associated to approximate computation of the permanent. But these bounds depend on geometric quantities such as the maximum degree, diameter and covering number of associated graphs.
Abstract: We develop bounds for the second largest eigenvalue and spectral gap of a reversible Markov chain. The bounds depend on geometric quantities such as the maximum degree, diameter and covering number of associated graphs. The bounds compare well with exact answers for a variety of simple chains and seem better than bounds derived through Cheeger-like inequalities. They offer improved rates of convergence for the random walk associated to approximate computation of the permanent.
947 citations
TL;DR: In this paper, it was shown that a queueing network is positive Harris recurrent if the corresponding fluid limit model eventually reaches zero and stays there regardless of the initial system configuration, and that single class networks, multiclass feedforward networks and first-buffer-first-served preemptive resume discipline in a reentrant line are positive Harris-rewarded under the usual traffic condition.
Abstract: It is now known that the usual traffic condition (the nominal load being less than 1 at each station) is not sufficient for stability for a multiclass open queueing network. Although there has been some progress in establishing the stability conditions for a multiclass network, there is no unified approach to this problem. In this paper, we prove that a queueing network is positive Harris recurrent if the corresponding fluid limit model eventually reaches zero and stays there regardless of the initial system configuration. As an application of the result, we prove that single class networks, multiclass feedforward networks and first-buffer-first-served preemptive resume discipline in a reentrant line are positive Harris recurrent under the usual traffic condition.
927 citations