Journal article
NONLINEAR FEYNMAN-KAC FORMULAS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH SPACE-TIME NOISE
SIAM journal on mathematical analysis, v 51(2), pp 955-990
01 Jan 2019
Abstract
We study a class of backward doubly stochastic differential equations involving martingales with spatial parameters, and show that they provide probabilistic interpretations (Feynman- Kac formulas) for certain semilinear stochastic partial differential equations (SPDEs) with space-time noise. As an application of the Feynman-Kac formulas, random periodic solutions and stationary solutions to certain SPDEs are obtained.
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Details
- Title
- NONLINEAR FEYNMAN-KAC FORMULAS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH SPACE-TIME NOISE
- Creators
- Jian Song - Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R ChinaXiaoming Song - Drexel UniversityQi Zhang - Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
- Publication Details
- SIAM journal on mathematical analysis, v 51(2), pp 955-990
- Publisher
- Siam Publications
- Number of pages
- 36
- Grant note
- 11471079; 11631004; 11871163 / National Natural Science Foundation of China; National Natural Science Foundation of China (NSFC)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000464913300012
- Scopus ID
- 2-s2.0-85065505917
- Other Identifier
- 991019167606304721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied