Stochastic Partial Differential Equations and Invariant Manifolds in Embedded Hilbert Spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.