ABSTRACT

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.

中文翻译：

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广义灰色布朗运动的积分表示。

摘要

在本文中，我们根据随机过程的加权积分来研究一类非高斯过程，即广义灰色布朗运动，该过程是某个随机微分方程的解。特别地，基础过程可以看作是Ornstein–Uhlenbeck过程的非高斯扩展，因此可以概括为俄罗斯数学Muravlev的表示结果。调查66（2），2011年以及危害和Stefanovits，随机过程。应用 129，2019至非高斯案。