The study of asymptotic behavior of Wiener sausages for stochastic processes

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540181
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kumamoto University
• Principal Investigator: Hamana Yuji 熊本大学, 自然科学研究科, 教授 (00243923)
• Research Collaborator: MATSUMOTO Hiroyuki
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 確率論 / 確率解析 / ベッセル過程 / 到達時刻 / Wiener sausage / 変形ベッセル関数

Outline of Final Research Achievements

We give the joint distribution of the hitting time and site of a Brownian motion with and without constant drift. This result yields the formula for the expected volume of the Wiener sausages of Brownian motions and their asymptotic behavior for large time. Moreover we obtain the asymptotics of tail probabilities of first hitting times of Bessel processes with and without the drift. In addition, we find that zeros of Bessel function of the second kind are holomorhic with respect to the indices and establish the method of their calculation with a general-purpose computer soft of computations, Mathematica for example.

Free Research Field

確率論