Stochastic Partial Differential Equations and Invariant Manifolds in Embedded Hilbert Spaces

IF 1 3区数学 Q1 MATHEMATICS

Potential Analysis Pub Date : 2024-05-11 DOI:10.1007/s11118-024-10134-8

Rajeev Bhaskaran, Stefan Tappe

引用次数: 0

Abstract

We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds for solutions of stochastic partial differential equations (SPDEs) in continuously embedded Hilbert spaces with non-smooth coefficients. Furthermore, we establish a link between invariance of submanifolds for such SPDEs in Hermite Sobolev spaces and invariance of submanifolds for finite dimensional SDEs. This provides a new method for analyzing stochastic invariance of submanifolds for finite dimensional Itô diffusions, which we will use in order to derive new invariance results for finite dimensional SDEs.

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嵌入希尔伯特空间中的随机偏微分方程和不变曲率

我们为具有非光滑系数的连续嵌入希尔伯特空间中的随机偏微分方程（SPDE）解的有限维子实体的随机不变性提供了必要和充分条件。此外，我们还建立了赫米特索波列夫空间中此类 SPDE 的子实体不变性与有限维 SDE 的子实体不变性之间的联系。这为分析有限维 Itô 扩散的子曼形体的随机不变性提供了一种新方法，我们将利用这种方法推导出有限维 SDE 的新不变性结果。

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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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.