Asymptotic Estimates of the Distribution of Brownian Hitting Time of a Disc

作者：Uchiyama Kohei^*

来源：Journal of Theoretical Probability, 2012, 25(2): 450-463.

DOI：10.1007/s10959-010-0305-8

• Brownian hitting time
• Asymptotic expansion
• Fourier analysis
• Laplace inversion

The distribution of the first hitting time of a disc for the standard two-dimensional Brownian motion is computed. By investigating the inversion integral of its Laplace transform we give fairly detailed asymptotic estimates of its density valid uniformly with respect to the point from which the Brownian motion starts.

• 出版日期2012-6