We prove the large deviation principle for the law of the one-dimensional semi-linear stochastic partial differential equations driven by a nonlinear multiplicative noise.Firstly,combining the energy estimate and appr...We prove the large deviation principle for the law of the one-dimensional semi-linear stochastic partial differential equations driven by a nonlinear multiplicative noise.Firstly,combining the energy estimate and approximation procedure,we obtain the existence of the global solution.Secondly,the large deviation principle is obtained via the weak convergence method.展开更多
We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent t...We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent to the Antosik-Mikusinski theorems.展开更多
基金supported in part by the NSFC Grant No.12171084the fundamental Research Funds for the Central Universities No.2242022R10013.
文摘We prove the large deviation principle for the law of the one-dimensional semi-linear stochastic partial differential equations driven by a nonlinear multiplicative noise.Firstly,combining the energy estimate and approximation procedure,we obtain the existence of the global solution.Secondly,the large deviation principle is obtained via the weak convergence method.
基金This project is supported by NSFC(10471124)is supported by Zhejiang Provineial Natural Science Foundation of China(M103057)sponsored by SRF for ROCS,SEM
文摘We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent to the Antosik-Mikusinski theorems.
