We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional sto...We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional stochastic differential equations driven by Poisson processes. After that, we give a simplified Engelbert theorem for the stochastic differential equations of this type.展开更多
The authors construct a solution U_t(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a s...The authors construct a solution U_t(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity,namely one-fold differentiability.Besides,the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.展开更多
The existence and uniqueness of solutions to the multivalued stochastic differential equations with non-Lipschitz coeffcients are proved,and bicontinuous modifications of the solutions are obtained.
文摘We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
文摘We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional stochastic differential equations driven by Poisson processes. After that, we give a simplified Engelbert theorem for the stochastic differential equations of this type.
基金Project supported by the National Natural Science Foundation of China(Nos.11171358,11026202,11101441)the Doctor Fund of Ministry of Education(Nos.20100171110038,20100171120041)the Natural Science Foundation of Guangdong Province(No.S2012040007458)
文摘The authors construct a solution U_t(x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity,namely one-fold differentiability.Besides,the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.
基金supported by the National Natural Science Foundation of China (No.10871215).
文摘The existence and uniqueness of solutions to the multivalued stochastic differential equations with non-Lipschitz coeffcients are proved,and bicontinuous modifications of the solutions are obtained.
