Averaging for slow–fast piecewise deterministic Markov processes with an attractive boundary

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Applied Probability Pub Date : 2023-05-19 DOI:10.1017/jpr.2023.8

A. Genadot

引用次数: 0

Abstract

In this paper we consider the problem of averaging for a class of piecewise deterministic Markov processes (PDMPs) whose dynamic is constrained by the presence of a boundary. On reaching the boundary, the process is forced to jump away from it. We assume that this boundary is attractive for the process in question in the sense that its averaged flow is not tangent to it. Our averaging result relies strongly on the existence of densities for the process, allowing us to study the average number of crossings of a smooth hypersurface by an unconstrained PDMP and to deduce from this study averaging results for constrained PDMPs.

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具有吸引边界的慢速-快速分段确定性Markov过程的平均

本文研究了一类动态受边界约束的分段确定性马尔可夫过程的平均问题。在到达边界时，过程被迫跳出边界。我们假设这个边界对所讨论的过程是有吸引力的，因为它的平均流量与它不相切。我们的平均结果在很大程度上依赖于密度的存在，这使我们能够研究无约束PDMP在光滑超表面上的平均交叉次数，并从这项研究中推断出有约束PDMP的平均结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.