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On the equivalence of pathwise mild and weak solutions for quasilinear SPDEs
Stochastic Analysis and Applications ( IF 0.8 ) Pub Date : 2020-12-17 , DOI: 10.1080/07362994.2020.1857268 Gaurav Dhariwal 1 , Florian Huber 1 , Alexandra Neamţu 2
中文翻译:
关于拟线性SPDE的路径弱解和弱解的等价性
更新日期:2020-12-17
Stochastic Analysis and Applications ( IF 0.8 ) Pub Date : 2020-12-17 , DOI: 10.1080/07362994.2020.1857268 Gaurav Dhariwal 1 , Florian Huber 1 , Alexandra Neamţu 2
Affiliation
Abstract
The main goal of this work is to relate weak and pathwise mild solutions for parabolic quasilinear stochastic partial differential equations (SPDEs). Extending in a suitable way techniques from the theory of nonautonomous semilinear SPDEs to the quasilinear case, we prove the equivalence of these two solution concepts.
中文翻译:
关于拟线性SPDE的路径弱解和弱解的等价性
摘要
这项工作的主要目标是关联抛物线拟线性随机偏微分方程 (SPDE) 的弱解和路径温和解。以合适的方式将技术从非自治半线性 SPDE 理论扩展到拟线性情况,我们证明了这两个解决方案概念的等价性。