Keynote Speaker:Wu Fuke

Abstract:

Dupire recently developed a functional It\^o formula, which has changed the landscape of the study of stochastic functional equations and encouraged a reconsideration of many problems and applications. Delays are ubiquitous, pervasive, and entrenched in everyday life. Based on the new development, this work examines functional diffusions with two-time scales in which the slow-varying process includes path-dependent functionals and the fast-varying process is a rapidly-changing diffusion. The gene expression of biochemical reactions occurring in living cells in the introduction of this paper is such a motivating example. This paper establishes mixed functional Ito formulas and the corresponding martingale representation. Then it develops averaging and weak convergence methods. By treating the fast-varying process as a random ``noise", under appropriate conditions, it is shown that the slow-varying process converges weakly to a stochastic functional differential equation whose coefficients are averages of that of the original slow-varying process with respect to the invariant measure of the fast-varying process.

Introduction to the Speaker:

Wu Fuke, professor of School of Mathematics and Statistics, Huazhong University of Science and Technology, doctoral supervisor, was selected into "New Century Excellent Researcher Award Program" of the Ministry of Education in 2011, the "scholar of HUST" of Huazhong University of Science and Technology in 2012, the "Outstanding Youth Fund" of the Fund Committee in 2014, the second prize of the Hubei Provincial Natural Science Award in 2015, the "Newton Advanced Fellowship" Fund of The Royal Society in 2017, and the editorial board member of SCI journalIET Control Theory & Applications.

Inviter:

Chen Zhang, Professor of School of Mathematics

Time:

10:00-11:00 on December 4 (Friday)

Location:

Tencent Meeting, ID: 332594762

Sponsored by: School of Mathematics, Shandong University