Hitting times of Bessel processes, volume of Wiener sausages and zeros of Macdonald functions

2013/02/19 by Yuji Hamana, Hamana, Yuji, Hiroyuki Matsumoto +1
Computer Science · Mathematics · #33C10 (primary) #41A60 #60E07 #60G99 (secondary) #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1302.4526

openalex publication_date 2013/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive formulae for some ratios of the Macdonald functions, which are simpler and easier to treat than known formulae. The result gives two applications in probability theory. One is the formula for the Lévy measure of the distribution of the first hitting time of a Bessel process and the other is an explicit form for the expected volume of the Wiener sausage for an even dimensional Brownian motion. Moreover, the result enables us to write down the algebraic equations whose roots are the zeros of Macdonald functions.

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