报告题目：The first exit time of a Brownian motion
报 告 人：鲁大伟 （大连理工大学）
Comparing with the results of Li (2003), in this talk, we consider the first exit time of a Brownian motion with increasing dimensions from an unbounded convex domain, namely the dimension d in Li (2003) is replaced by d(s), which is a non-decreasing integral function. Combining some new properties of Bessel function which we found, the results in Li (2003) and Gaussian techniques, we obtain very general upper and lower estimates for the probability of the first exit time of a Brownian motion with increasing dimensions. Furthermore, in some specific domain, we prove that the upper and lower estimates are asymptotically equivalent.