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学术活动
Probabilistic limit behaviors of numerical discretizations for time-homogeneous Markov processes
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报告人:
Guoting Song, Doctor, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
题目:
Probabilistic limit behaviors of numerical discretizations for time-homogeneous Markov processes
时间地点:
16:00-17:00 December 20 (Wednesday), Z311
摘要:

In order to give quantitative estimates for approximating the ergodic limit, we investigate probabilistic limit behaviors of time-averaging estimators of numerical discretizations for a class of time-homogeneous Markov processes, by studying the corresponding strong law of large numbers and the central limit theorem. Verifiable   general sufficient conditions are proposed to ensure these limit behaviors, which are related to the properties of strong mixing and strong convergence for numerical discretizations of Markov processes. Our results hold for test functionals with lower regularity compared with existing results, and the analysis does not require the existence of the Poisson equation associated with the underlying Markov process. Notably, our results are applicable to numerical discretizations for a large class of stochastic systems, including stochastic ordinary differential equations, infinite dimensional stochastic evolution equations, and stochastic functional differential equations.