广义灰色布朗运动的积分表示。

Stochastics (Abingdon, England : 2005) Pub Date : 2019-07-11 DOI:10.1080/17442508.2019.1641093

Wolfgang Bock, Sascha Desmettre, José Luís da Silva

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摘要

在本文中，我们研究了一类非高斯过程（即广义灰色布朗运动）的表示方法，即随机过程的加权积分，它是某个随机微分方程的解。特别是，基础过程可以看作是奥恩斯坦-乌伦贝克过程的非高斯扩展，从而推广了穆拉夫列夫的表示结果，《俄罗斯数学》，第 66 (2) 卷，第 2 期，第 2 页。Surveys 66 (2), 2011 以及 Harms 和 Stefanovits, Stochastic Process.应用》，2019 年第 129 期，适用于非高斯情况。

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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Integral representation of generalized grey Brownian motion.

In this paper, we investigate the representation of a class of non-Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular, the underlying process can be seen as a non-Gaussian extension of the Ornstein-Uhlenbeck process, hence generalizing the representation results of Muravlev, Russian Math. Surveys 66 (2), 2011 as well as Harms and Stefanovits, Stochastic Process. Appl. 129, 2019 to the non-Gaussian case.

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