Mini-course: Stochastic differential equations with H older continuous coefficients - PDE vs Geometry

Thời gian: 14:00 đến 16:00 ngày 11/04/2017, 09:00 đến 11:00 ngày 13/04/2017, 14:00 đến 16:00 ngày 18/04/2017, 09:00 đến 11:00 ngày 27/04/2017,

Địa điểm: C2-714, VIASM

Tóm tắt:

Aim: In this course, I will consider some stochastic differential equations with Holder continuous coefficients derived from mathematical models in biology. From PDE point of view, we will derive singular Kolmogorov equations on manifolds with corners. I will discuss on difficulties in studying such equations as well as how to overcome them. 
From geometrical point of view, I will first introduce the information geometry theory and how to apply it in our problem. I will then mention to a powerful approach of free energy functional to study the convergence rate to the invariant measure as well as connect it to gradient flow theory.

Outline of the course (intended):

 Day 1 (14-16 : 11 April, 2017): Background, motivation, some approaches to SDEs with Holder continuous coefficients.
 Day 2 (9-11  : 13 April, 2017): PDE approach: the existence, uniqueness and regularity of solutions.
 Day 3 (14-16: 18 April, 2017): Geometric approach: Information geometry and its applications.
 Day 4 (9-11  : 27 April, 2017): Geometric approach: Free energy functional and the Fisher-Wasserstein gradient flow.