1. 报告题目：A Kernel Method for Random Walks in the Quarter Plane

central focuses in probability, particularly in applied probability. Two-dimensional random walks are such examples. In this talk, we discuss stationary tail asymptotic properties for random walks in the quarter plane, which are random walks with reflective boundaries and find many important applications such as queueing systems. For a stable system, say a discrete-time ergodic two-dimensional (the state space in the quarter plane) Markov chain, the unique stationary distribution is one of the key performance metrics. However, except very few special cases, no closed form or explicit solutions for such systems. For this reason and also with its own importance, behaviour of tail asymptotics in the joint stationary distribution is a key topic in applied probability. We introduce a kernel method to study the behaviour and show that there is a total of four different types of tail asymptotics.

Based on joint work with Hui Li, Javad Tavakoli, and many others.

1. 报告题目 D-Dimensional Sticky Brownian Motions: Some Conjectures

Sticky Brownian motions as time-changed semimartingale reflecting Brownian motions have important applications in many fields such as queuing theory and mathematical finance. In this talk, we are concerned with stationary distributions of a general multidimensional sticky Brownian motion provided it is stable. We conjecture tail behaviors of their stationary distributions. Due to recent studies, these conjectures are true for some special cases.

1. 报告题目: A Complete Solution to Mean Field Linear Quadratic Control

1. 报告题目：Necessary Conditions for the Compensation Approach for a Random Walk in the Quarter-plane

1. 报告题目：$\beta$-Invariant Measures and Quasi-Stationary

Distributions for Block-Structured Markov Chains

Based on joint work with Q-L Li.

1. 报告题目：Quasi-stationarity and Quasi-ergodicity of Absorbing Markov

Processes.

1. 报告题目：Transience Classification for Block-structured Markov Chains

报告人：李文迪 博士生， 中南大学

报告摘要M/G/1-type and GI/M/1-type Markov chains are level independent matrix analytical models, which have proved very useful for characterizing the phase type queues. Stability properties have been investigated well for M/G/1 and GI/M/1-type Markov chains. In this talk, we will present explicit criteria for classification of instability including geometric transience and algebraic transience for these Markov chains. Possible extensions of the results to continuous-time Markov chains are also considered. The radius of convergence and the expression of quasi-stationary distribution are also examined for some special cases.

报告人简介：李文迪，中南大学在读博士，主要从事马氏过程稳定性及相关领域研究。