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Support theorem for an SPDE with multiplicative noise driven by a cylindrical Wiener process on the real line
Stochastics and Partial Differential Equations: Analysis and Computations ( IF 1.4 ) Pub Date : 2019-09-18 , DOI: 10.1007/s40072-019-00152-8
Timur Yastrzhembskiy

We prove a Stroock–Varadhan’s type support theorem for a stochastic partial differential equation on the real line with a noise term driven by a cylindrical Wiener process on \(L_2 ({\mathbb {R}})\). The main ingredients of the proof are V. Mackevičius’s approach to support theorem for diffusion processes and N.V. Krylov’s \(L_p\)-theory of SPDEs.



中文翻译:

在实线上由圆柱维纳过程驱动的带乘性噪声的SPDE的支持定理

我们证明了实线上的随机偏微分方程的Stroock-Varadhan型支持定理,其中噪声项由\(L_2({\ mathbb {R}})\)上的圆柱维纳过程驱动。证明的主要成分是V.Mackevičius的支持扩散过程定理的方法和SPDE的NV Krylov的\(L_p \)-理论。

更新日期:2019-09-18
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