在无界凸区域上多个布朗运动之和首冲时

The first exit time of sum of Brownian motions from unbounded convex domain

考虑在无界区域中Bessel函数下多个布朗运动和的首冲时问题.介绍了利用高斯计算技巧和Slepian不等式得到的单个布朗运动在无界开区域Rd+1中首冲时的上﹑下界的渐近估计,然后考虑了多个布朗运动的和在Bessel函数下首冲时的上﹑下界渐近估计.首先考虑在移动边界下的首冲时问题,之后再推广到无界区域中多个布朗运动的和.说明单个的布朗运动首冲时问题,可以推广到多个布朗运动之和的首冲时问题.

The first exit time of the sum of several Brownian motions in the case of Bessel function from an unbounded domain is considered.Firstly,general upper and lower asymptotic estimates for the first exit time of one Brownian motion from an unbounded open domain Rd＋1 are obtained,which are based on a powerful Gaussian technique and Slepian′s inequality.Then,the general upper and lower asymptotic estimates are considered to the first exit time of the sum of several Brownian motions in the case of Bessel function.At first,the first exit time probability with moving boundary is considered,then,it′s extended to the sum of the number of Brownian motions in the unbounded domain.It means that the first exit time of one Brownian motion is suitable for the first exit time of the sum of several Brownian motions.