浙江大学---复旦大学概率统计联合讨论班

浙江大学---复旦大学概率统计联合讨论班

时间：2018年4月21日

地点：浙江大学玉泉校区欧阳纯美楼316

上午  主持人： 苏中根  浙江大学

10:00-10:45     沈云骢    复旦大学

题目：Excessive measures for linear diffusions

11:00-11:45    李利平  中国科学院

题目: On stiff problems via Dirichlet forms

下午   主持人：应坚刚   复旦大学

14:00-15:00   Jordan Stoyanov    山东大学访问教授

题目：Distributions and Moments: Characterizations and Limit Theorems

15:15-16:00    孟庆欣    湖州师范学院

题目：Maximum principle for mean-field jump�diffusion stochastic delay differential equations and its application to finance

Excessive measures for linear diffusions

                    沈云骢

Excessive measures play an important role in the study of Markov processes. However, there are few works about the existence of excessive measures. In this paper, we give a necessary and sufficient condition for a linear diffusion to possess a fully supported excessive measure.

On stiff problems via Dirichlet forms

李利平

The stiff problem is concerned with the thermal conduction model with a very small barrier, which is treated as a singular material with zero volume and zero thermal conductivity. In this talk, we shall build a phase transition for the stiff problems in one-dimensional space and that related to the Walsh’s Brownian motion. It turns out that the phase transition fairly depends on the total thermal resistance of the barrier, and the three phases corresponds to the so-called adiabatic pattern, penetrable pattern and diffusive pattern of the thermal conduction respectively. For each pattern, the related boundary condition at the barrier of the thermal conduction will be also derived. Mathematically, we shall also introduce and explore the so-called snapping out Markov process, which is the probabilistic counterpart of penetrable pattern for the stiff problems. 

Distributions and Moments: Characterizations and Limit Theorems 

                Jordan Stoyanov

We deal with random variables and their distributions, 1-dimensional or multidimensional, discrete or continuous, assuming they have finite all integer positive order moments. Any such a distribution is either uniquely determined by its moments, and we say that it is M-determinate, or it is non-unique, M-indeterminate. 

For an absolutely continuous M-indeterminate distribution F, we show how to construct Stieltjes classes of infinitely many distributions all having the same moments as F.  

We will discuss some recent and “easily checkable conditions” which are either sufficient or necessary to characterize a distribution as being M-determinate or M-indeterminate. The results will be illustrated by examples and counterexamples.  There will be new and not so well-known facts for popular distributions, some are unexpected, even shocking.

The well-known Frechet-Shohat theorem involves essentially the M-determinacy. Two specific stochastic models will be analyzed by describing explicitly the limit laws.

If time permits, a few open questions will be outlined. 

Maximum principle for mean-field jump-diffusion stochastic delay differential equations and its application to finance

              孟庆欣

This paper investigates a stochastic optimal control problem with delay and of mean-field type, where the controlled state process is governed by a mean-field jump-diffusion stochastic delay differential equation. Two sufficient maximum principles and one necessary maximum principle are established for the underlying system. As an application, a bicriteria mean variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques. Under certain conditions, explicit expressions are provided for the efficient portfolio and the efficient frontier, which are as elegant as those in the classical mean-variance problem without delays.

联系人：赵敏智（zhaomz@zju.edu.cn） 

欢迎广大师生参加！