ome

# 【1月12日-1月14日】随机方程研讨会

 1月13日 报告人 报告题目 08:30–09:20 董昭 The concentration of limiting invariant measure for stochastic dynamic system with local Lipschitz coefficients in 09:30–10:20 刘伟（武汉大学） Long-time behavior of mean-field interacting particle systems related to McKean-Vlasov equation 10:30–11:20 刘伟（江苏师范大学） Asymptotics of Multiscale Stochastic Systems 14:00–14:50 张希承 Heavy-tailed sampling via SDEs 15:00–15:50 谢颖超 随机微分方程平均化原理的一些研究 16:00–16:50 王健 Continuous-state branching processes with immigration and competition 17:00–17:30 尚世界 Well-posedness to stochastic partial differential equations with locally monotone coefficients

The concentration of limiting invariant measure for stochastic dynamic system with local Lipschitz coefficients in

Abstract: In this talk, I consider the zero-noise limit of the invariant measure  of the SDE defined on with local Lipschitz coefficients and more than one ergodic state. Our result illustrates that, under some certain conditions, the  weakly converges to a linear combination of Dirac measure, which supports on some stable sets of the corresponding ODE. To make our result more intuitive,I will first give some numerical simulations of examples. Secondly, I will present the main results of our work with brief proofs, which are generalizations of the classic Freidlin-Wentzell theory.

Finally, I will analyze the examples above theoretically. This talk is based on the joint work with Fan Gu and Liang Li.

Long-time behavior of mean-field interacting particle systems related to McKean-Vlasov equation

Abstract: In this talk, we will show concentration inequalities, exponential convergence in the Wasserstein metric $W_{1}$, and uniform-in-time propagation of chaos for the mean-field weakly interacting particle system related to McKean-Vlasov equation. By means of the known approximate componentwise reflection coupling and with the help of some new cost function, we obtain explicit estimates for those three problems, avoiding the technical conditions in the known results. Our results apply to possibly multi-well confinement potentials, and interaction potentials $W$ with bounded second mixed derivatives $\nabla^2_{xy}W$ which are not too big, so that there is no phase transition. Several examples are provided to illustrate the results.  This is a joint work with L. Wu and C. Zhang.

Asymptotics of Multiscale Stochastic Systems

Abstract: In this talk we mainly present some asymptotic results for a class of multiscale stochastic systems, more precisely, we will show some strong averaging principle, large deviations principle and central limit type theorems for multiscale SPDEs and DDS(P)DEs.

Heavy-tailed sampling via SDEs

Abstract: In this work we put forward a new algorithm for heavy-tailed sampling via multiplicaitive SDEs driven by $\alpha$-stable processes.

Continuous-state branching processes with immigration and competition

Abstract: To model stationary population dynamics with competitions between individuals, we include immigration structure into branching processes with competition introduced by Berestycki et al. (2018).  Such processes are constructed as pathwise unique solutions of stochastic integral equations driven by Brownian motions and Poisson random measures. By constructing novel cost functions and adopting Markov coupling techniques, we present sufficient conditions for the exponential ergodicity both in the Wasserstein distance and the weighted total variation distance. The $C_b$-Feller property and the property of coming down from infinity are also investigated. This talk is based on the joined work with Pei-Sen Li, Zenghu Li and Xiaowen Zhou.

Well-posedness to stochastic partial differential equations with locally monotone coefficients

Abstract: In this paper, we consider SPDEs driven by multiplicative noise with locally monotone coefficients. We established the well-posedness of solutions to the equations under rather weak local monotone conditions.