非平凡分数噪声驱动随机演化方程集值动力系统的随机吸引子

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Stochastics and Dynamics Pub Date : 2022-05-14 DOI:10.1142/s0219493722400184

M. Garrido-Atienza, B. Schmalfuss, J. Valero

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引用次数: 2

摘要

我们考虑一个由分数布朗运动驱动的随机演化方程在可分离的希尔伯特空间与赫斯特参数[公式:见文本]。噪声前的系数一般是非线性的。相关积分是由分数阶导数定义的路径积分。该方程的非线性系数满足仅解存在而不唯一的弱条件。该方程生成了一个多值随机动力系统。证明了该系统的随机吸引子的存在性。

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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Random attractors for setvalued dynamical systems for stochastic evolution equations driven by a nontrivial fractional noise

We consider a stochastic evolution equation driven by a fractional Brownian motion in a separable Hilbert space with Hurst parameter [Formula: see text]. The coefficient in front of the noise is in general nonlinear. The related integral is a pathwise integral defined by fractional derivatives. The nonlinear coefficients of this equation satisfy weak conditions ensuring only existence of a solution but not uniqueness. This equation generates then a multivalued random dynamical system. We prove the existence of a random attractor for this system.

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来源期刊

Stochastics and Dynamics 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view. Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.