Speaker: Prof. Jianguo Liu（刘建国教授）

Time: 10:30-11:30, 24 November 2023 (Friday) (Beijing time)

Venue: 华信书院，CC126

Tencent Meeting ID: 696-207-641

Abstract

We focus on the transition path problem and mean field games for Markov jump processes on graph and in general on any Borel space. We first formulate the transition path problem for Markov jump processes as a stochastic optimal control problem in an infinite time horizon. Using the Girsanov transformation for pure jump processes, we choose the certain relative-entropy type running cost and a terminal cost for the stochastic optimal control problem with a stopping time. Unbounded terminal cost serves as a hard constraint, which guarantees the almost sure transition between metastable sets and can be taken care using Gamma -convergence. We prove a closed formula solution for optimal control computed via the discrete committor function. In the deterministic finite time horizon, both transition path and mean field game problem can be formulated as convex optimization for measures. Moreover, disintegration formula puts both finite time and infinite time (stochastic) optimal control into one framework, which are convex optimization problem for path measures.

About Prof. Liu

刘建国教授在杜克大学任教数学与物理，并同时担任杜克昆山大学祖冲之数学与计算科学中心的联合主任。他在复旦大学获得了本科和硕士学位，并随后在加利福尼亚大学洛杉矶分校取得博士学位。

作为美国数学会的Fellow，刘教授的研究领域涵盖了复杂方程在流体动力学、材料科学、生物学和机器学习等多个领域的应用。最近，他特别关注最优控制和哈密尔顿-雅可比方程在各科学领域的应用。他是《The Journal of Hyperbolic Differential Equations 》的创始编辑之一，已连续20年作为该杂志的联合编辑。