主講人：Renming-Song
講座題目：Harnack principle for symmetric stable processes and subordinate Brownian motion
時　　間：2012年7月23，24，25, 27日上午10:40~12:00, 及7月30, 31日上午9：00~11:00.
地　　點：研究生樓209A
主講人介紹
　　Renming-Song received the B.S. degree in mathematics in 1983 and M.S. degree in Mathemtics in 1986, both from Hebei University, Baodin, China. He received his Ph.D. degree in Mathematics from the University of Florida, Gainesville in 1993. He was a visiting assistant professor at Northwestern University and the University of Michigan before moving to the University of Illinois in 1997, where he is a Professor of Mathematics since 2009.
　　His research interests include stochastic analysis, Markov processes, potential theory and financial mathematics. Renming Song has published more than 77 research papers, in top mathematical Journals.
主要內(nèi)容：Recently many breakthroughs have been made in the potential theory of symmetric stable processes and subordinate Brownian motions. In all these recent developments, the boundary Harnack principle played an essential role. In this series of lectures I plan to give a self-contained account of the boundary Harnack principle for symmetric stable processes. Then I will extend the argument to obtain the boundary Harnack principle
for a large class of subordinate Brownian motions.

Here are some references:

[1]. K. Bogdan. The boundary Harnack principle for the fractional Laplacian. Studia Math. (1997), 43--80.
[2]. P. Kim, R. Song and Z. Vondracek. Boundary Harnack Principle for Subordinate Brownian Motions. Stoch. Proc. Appl. 119 (2009), 1601--1631.
[3]. P. Kim, R. Song and Z. Vondracek. Potential theory of subordinate Brownian motions revisited. To appear in Stochastic Analysis and Applications to Finance--Essays in Honour of Jia-an Yan, edited by Tusheng Zhang and Xunyu Zhou. World Scientific,2012.
[4]. R. Song. Potential theory of subordinate Brownian motions.
http://open.nims.re.kr/download/probability/song.pdf
[5]. R. Song and J.-M. Wu. Boundary Harnack inequality for symmetric stable processes. J. of Funct. Anal. 168 (1999),403-427.