Stochastic Partial Differential Equations and Invariant Manifolds in Embedded Hilbert Spaces

被引：1

作者：

Bhaskaran, Rajeev ^{[1
]}

Tappe, Stefan ^{[2
]}

机构：

[1] Indian Inst Sci Educ & Res Thiruvanantapuram, Sch Math, Chennai 695551, Kerala, India

[2] Albert Ludwig Univ Freiburg, Dept Math Stochast, Ernst Zermelo Str 1, D-79104 Freiburg, Germany

来源：

POTENTIAL ANALYSIS | 2025年 / 62卷 / 01期

关键词：

Stochastic partial differential equation; Continuously embedded Hilbert spaces; Invariant manifold; Finite dimensional diffusion; Multi-parameter group; Hermite Sobolev space; Translation invariant solution; FINITE-DIMENSIONAL REALIZATIONS; AFFINE REALIZATIONS; TERM STRUCTURE; PROBABILISTIC REPRESENTATIONS; EXISTENCE; DIFFUSIONS; GEOMETRY; SETS;

D O I：

10.1007/s11118-024-10134-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 It & ocirc; diffusions, which we will use in order to derive new invariance results for finite dimensional SDEs.

引用

页码：189 / 236

页数：48

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