This work is concerned with the continuous dependence on initial values of solutions of stochastic functional differential equations(SFDEs) with state-dependent regime-switching. Due to the state-dependence, this prob...This work is concerned with the continuous dependence on initial values of solutions of stochastic functional differential equations(SFDEs) with state-dependent regime-switching. Due to the state-dependence, this problem is very different to the corresponding problem for SFDEs without switching or SFDEs with Markovian switching. We provide a method to overcome the intensive interaction between the continuous component and the discrete component based on a subtle application of Skorokhod’s representation for jumping processes. Furthermore, we establish the strong convergence of Euler–Maruyama’s approximations, and estimate the order of error. The continuous dependence on initial values of Euler–Maruyama’s approximations is also investigated in the end.展开更多
In this paper, the dimensional-free Harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhle...In this paper, the dimensional-free Harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy ＂H＂, Wasserstein distance ＂W＂, and Fisher information ＂T＂.展开更多
In this work, by constructing optimal Markovian couplings we investigate exponential convergence rate in the Wasserstein distance for the transmission control protocol process. Most importantly, we provide a variation...In this work, by constructing optimal Markovian couplings we investigate exponential convergence rate in the Wasserstein distance for the transmission control protocol process. Most importantly, we provide a variational formula for the lower bound of the exponential convergence rate.展开更多
基金Supported in part by NNSFs of China(Grant Nos.11771327,11431014,11831014)。
文摘This work is concerned with the continuous dependence on initial values of solutions of stochastic functional differential equations(SFDEs) with state-dependent regime-switching. Due to the state-dependence, this problem is very different to the corresponding problem for SFDEs without switching or SFDEs with Markovian switching. We provide a method to overcome the intensive interaction between the continuous component and the discrete component based on a subtle application of Skorokhod’s representation for jumping processes. Furthermore, we establish the strong convergence of Euler–Maruyama’s approximations, and estimate the order of error. The continuous dependence on initial values of Euler–Maruyama’s approximations is also investigated in the end.
基金Supported by National Natural Science Foundation of China （Grant No. 10721091） and the 973-Project （Grant No. 2006CB805901）
文摘In this paper, the dimensional-free Harnack inequalities are established on infinite-dimen- sional spaces. More precisely, we establish Harnack inequalities for heat semigroup on based loop group and for Ornstein-Uhlenbeck semigroup on the abstract Wiener space. As an application, we establish the HWI inequality on the abstract Wiener space, which contains three important quantities in one inequality, the relative entropy ＂H＂, Wasserstein distance ＂W＂, and Fisher information ＂T＂.
基金Supported NNSF of China(Grant Nos.11771327,2018JJ2478,11831014,12071340)。
文摘In this work, by constructing optimal Markovian couplings we investigate exponential convergence rate in the Wasserstein distance for the transmission control protocol process. Most importantly, we provide a variational formula for the lower bound of the exponential convergence rate.
