关于马尔可夫可加过程和马尔可夫调制广义奥恩斯坦-乌伦贝克过程的积分矩

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2024-05-09 DOI:10.1016/j.spa.2024.104382

Anita Behme, Paolo Di Tella, Apostolos Sideris

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引用次数: 0

摘要

我们为马尔可夫调制广义奥恩斯坦-乌伦贝克过程的κ'th矩κ≥1及其静态分布建立了存在的充分条件，并推导出明确的公式。我们的推导依赖于关于马尔可夫加过程矩和（多维）马尔可夫加过程积分的新的一般结果。

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On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein–Uhlenbeck processes

We establish sufficient conditions for the existence, and derive explicit formulas for the $κ$ ’th moments, $κ \geq 1$ , of Markov modulated generalized Ornstein–Uhlenbeck processes as well as their stationary distributions. In particular, the running mean, the autocovariance function, and integer moments of the stationary distribution are derived in terms of the characteristics of the driving Markov additive process.

Our derivations rely on new general results on moments of Markov additive processes and (multidimensional) integrals with respect to Markov additive processes.

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.