数学
独特性
动力系统理论
遍历理论
分数布朗运动
随机动力系统
动力系统(定义)
赫斯特指数
希尔伯特空间
布朗运动
数学分析
度量空间
空格(标点符号)
线性动力系统
线性系统
物理
统计
哲学
量子力学
语言学
作者
Y. Chen,Hui Gao,María J. Garrido–Atienza,Björn Schmalfuß
出处
期刊:Cornell University - arXiv
日期:2013-01-01
被引量:2
标识
DOI:10.48550/arxiv.1305.6903
摘要
This article is devoted to the existence and uniqueness of pathwise solutions to stochastic evolution equations, driven by a H\"older continuous function with H\"older exponent in $(1/2,1)$, and with nontrivial multiplicative noise. As a particular situation, we shall consider the case where the equation is driven by a fractional Brownian motion $B^H$ with Hurst parameter $H>1/2$. In contrast to the article by Maslowski and Nualart, we present here an existence and uniqueness result in the space of H\"older continuous functions with values in a Hilbert space $V$. If the initial condition is in the latter space this forces us to consider solutions in a different space, which is a generalization of the H\"older continuous functions. That space of functions is appropriate to introduce a non-autonomous dynamical system generated by the corresponding solution to the equation. In fact, when choosing $B^H$ as the driving process, we shall prove that the dynamical system will turn out to be a random dynamical system, defined over the ergodic metric dynamical system generated by the infinite dimensional fractional Brownian motion
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