有限速度Markov切换Ornstein–Uhlenbeck过程驱动的随机进化的平稳密度函数

IF 0.3 Q4 STATISTICS & PROBABILITY

Random Operators and Stochastic Equations Pub Date : 2022-04-06 DOI:10.1515/rose-2022-2075

A. Pogorui, R. Rodríguez-Dagnino

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引用次数: 1

摘要

摘要在本文中，我们考虑了一种新的Ornstein–Uhlenbeck类型的电报过程。该过程是通过将电报过程以类似于从维纳过程中获得奥恩斯坦-乌伦贝克过程的方式进行推广而获得的，即通过添加与原点位移成比例的漂移系数。Ratanov在[N.Ratanov，Ornstein–Uhlenbeck有界变异过程，Methodol.Comput.Appl.Probab.232021，925–946]中首次引入了这一过程。我们得到了这个过程的无穷小算子，并给出了求其平稳概率密度的公式。我们同时考虑对称和非对称情况。

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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Stationary density function for a random evolution driven by a Markov-switching Ornstein–Uhlenbeck process with finite velocity

Abstract In this paper, we consider a new telegraph process of Ornstein–Uhlenbeck type. The process is obtained by generalizing the telegraph process in a similar manner to how the Ornstein–Uhlenbeck process was obtained from the Wiener process, namely by adding a drift coefficient proportional to a displacement from the origin. This process was first introduced by Ratanov in [N. Ratanov, Ornstein–Uhlenbeck process of bounded variation, Methodol. Comput. Appl. Probab. 23 2021, 925–946]. We obtain the infinitesimal operator of this process and we present formulas for finding its stationary probability density. We consider both the symmetric and asymmetric cases.

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来源期刊

Random Operators and Stochastic Equations STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

25.00%

发文量