In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochas...In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochastic nonlinear Schrodinger equations.It is shown that the stochasticmulti-symplecticmethod preserves themultisymplectic structure,the discrete charge conservation law,and deduces the recurrence relation of the discrete energy.Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.展开更多
The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodi...The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established.展开更多
基金supported by the NNSFC(No.11001009)supported by the Director Foundation of GUCAS,the NNSFC(No.11071251)supported by the Foundation of CAS and the NNSFC(No.11021101,No.91130003).
文摘In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochastic nonlinear Schrodinger equations.It is shown that the stochasticmulti-symplecticmethod preserves themultisymplectic structure,the discrete charge conservation law,and deduces the recurrence relation of the discrete energy.Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.
基金Supported by NSFC(Grant Nos.1131003,11626245 and 11571043)
文摘The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established.
