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SOME RECENT PROGRESS ON STOCHASTIC HEAT EQUATIONS 预览
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作者 胡耀忠 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第3期874-914,共41页
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc... This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution. 展开更多
关键词 GAUSSIAN random field GAUSSIAN noise STOCHASTIC partial differential EQUATION (stochastic heat equation) Feynman-Kac FORMULA for the solution Feynman- Kac FORMULA for the moments of the solution chaos expansion hypercontractivity moment bounds HOLDER CONTINUITY joint HOLDER CONTINUITY asymptotic behaviour Trotter-Lie FORMULA Skorohod integral
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