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

Yuji Hamana; Hiroyuki Matsumoto

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

机译：贝塞尔工艺的击中时间，维纳香肠的体积和麦克唐纳函数的零

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摘要

We derive formulae for some ratios of the Macdonald functions by using their zeros, which are simpler and easier to treat than known formulae. The result gives two applications in probability theory and one in classical analysis. We show a formula for the Levy measure of the distribution of the first hitting time of a Bessel process and an explicit form for the expected volume of the Wiener sausage for an even dimensional Brownian motion. In addition, we show that the complex zeros of the Macdonald functions are the roots of some algebraic equations with real coefficients.

机译：我们通过使用零值来导出Macdonald函数某些比率的公式，这些公式比已知公式更容易处理。结果在概率论中有两种应用，在古典分析中有一种。我们为贝塞尔过程的第一次命中时间分布的征费度量提供了一个公式，并为维纳香肠的预期体积均匀维数布朗运动提供了一个明确的形式。此外，我们证明了麦克唐纳函数的复零点是某些具有实系数的代数方程的根。

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来源
《Journal of the Mathematical Society of Japan》 |2016年第4期|1615-1653|共39页
作者
Yuji Hamana; Hiroyuki Matsumoto;
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作者单位

Department of Mathematics Faculty of Science Kumamoto University Kurokami 2-39-1 Kumamoto 860-8555, Japan;

College of Science and Engineering Aoyama Gakuin University 5-10-1 Fuchinobe, Chuo-ku Sagamihara-shi Kanagawa 252-5258, Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Bessel process; Levy measure; Macdonald function; Wiener sausage;

机译：贝塞尔法征税措施;麦克唐纳功能;维也纳香肠;

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1. The Brownian hitting distributions in space‐time of bounded sets and the expected volume of the Wiener sausage for a Brownian bridge [J] . Uchiyama K?hei Proceedings of the London Mathematical Society . 2018,第3期

机译：布朗击中有界集的时空的分布以及布朗桥的预期大量的维纳香肠
2. Studies on the Zeroes of Bessel Functions and Methods for Their Computation: IV. Inequalities, Estimates, Expansions, etc., for Zeros of Bessel Functions [J] . Kerimov M. K. Computational mathematics and mathematical physics . 2018,第1期

机译：贝塞尔函数零的研究及其计算方法：IV。对贝塞尔函数的零的不等式，估计，扩展等。
3. Long Time Behavior of the Volume of the Wiener Sausage on Dirichlet Spaces [J] . Okamura Kazuki Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis . 2020,第3期

机译：Diener Spaces上的维纳香肠的体积的长时间行为
4. Globally convergent algorithm to find the zeros of the cross-product of Bessel functions [C] . Sorolla E., Mattes M. 2011 International Conference on Electromagnetics in Advanced Applications . 2011

机译：全局收敛算法，查找贝塞尔函数的叉积的零点
5. Distribution of the first hitting time of diffusion processes. [D] . Nguyen, Andrew Loc. 2002

机译：扩散过程的第一次命中时间的分布。
6. Orthogonality Lommel integrals and cross product zeros of linear combinations of Bessel functions [O] . Christian H Ziener, Felix T Kurz, Lukas R Buschle, -1

机译：贝塞尔函数线性组合的正交性洛梅尔积分和叉积零
7. Hitting times of Bessel processes, volume of Wiener sausages and zeros of Macdonald functions [O] . Hamana, Yuji, Matsumoto, Hiroyuki 2013

机译：达到贝塞尔工艺的时间，维纳香肠和零的体积 macdonald的功能

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

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