标题： 分数布朗运动驱动的随机微分方程：Hurst参数的依赖性 显示英文标题

标题： Stochastic differential equations driven by fractional Brownian motion: dependence on the Hurst parameter

摘要： 自2000年初以来，以分数布朗运动作为随机性来源的随机模型变得流行起来。 分数布朗运动(fBm)是一种高斯过程，其协方差依赖于所谓的Hurst参数 $H\in (0,1)$。 因此，含有fBm的随机模型也依赖于Hurst参数 $H$，这些模型关于 $H$的稳定性是一个有趣且重要的问题。 近年来，对于几种随机模型，包括关于fBm的随机积分、由fBm驱动的随机微分方程(SDE)以及具有分数噪声的随机偏微分方程，在不同拓扑结构下（例如按分布或几乎处处）和有限时间与无限时间范围内，研究了Hurst参数的连续（甚至更平滑）依赖性。 在本文档中，我们概述了这些结果，并特别关注SDE模型。 显示英文摘要

摘要： Stochastic models with fractional Brownian motion as source of randomness have become popular since the early 2000s. Fractional Brownian motion (fBm) is a Gaussian process, whose covariance depends on the so-called Hurst parameter $H\in (0,1)$. Consequently, stochastic models with fBm also depend on the Hurst parameter $H$, and the stability of these models with respect to $H$ is an interesting and important question. In recent years, the continuous (or even smoother) dependence on the Hurst parameter has been studied for several stochastic models, including stochastic integrals with respect to fBm, stochastic differential equations (SDEs) driven by fBm and also stochastic partial differential equations with fractional noise, for different topologies, e.g., in law or almost surely, and for finite and infinite time horizons. In this manuscript, we give an overview of these results with a particular focus on SDE models.