Fractional telegraph-type equations and hyperbolic Brownian motion

被引：6

作者：

D'Ovidio, Mirko ^{[1
]}

Orsingher, Enzo ^{[2
]}

Toaldo, Bruno ^{[2
]}

机构：

[1] Univ Roma La Sapienza, Dept Basic & Appl Sci Engn, Rome, Italy

[2] Univ Roma La Sapienza, Dept Stat Sci, Rome, Italy

来源：

STATISTICS & PROBABILITY LETTERS | 2014年 / 89卷

关键词：

Riemann-Liouville fractional calculus; Hyperbolic Brownian motion; Telegraph processes; Subordinators; Time-changed processes; Hyperbolic Laplacian;

D O I：

10.1016/j.spl.2014.02.021

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper is devoted to the interplay between time-fractional telegraph-type equations and processes defined on the n-dimensional Poincare half-space W. We solve such equations and show that the solutions coincide with the law of the composition of a hyperbolic Brownian motion with the inverse of the sum of two independent stable subordinators. In the case n = 3, we obtain the explicit form of the solution of the above equation. (c) 2014 Elsevier B.V. All rights reserved.

引用

页码：131 / 137

页数：7

共 9 条

[1]

[Anonymous], 2006, Journal of the Electrochemical Society

[2]

D'Ovidio M., 2012, ARXIV12062511

[3]

Debiard A., 1976, THEOREMES COMPARISON, V12, P391

[4]

GERTSENSHTEIN ME, 1959, TEOR VEROYA PRIMEN, V4, P424

[5]

Getoor R.K., 1961, PAC J MATH, V11, P128

[6]

GRUET JC, 1996, STOCHASTICS STOCHAST, V56, P53

[7]

KARPELEVICH FI, 1959, TEOR VEROYA PRIMEN, V4, P432

[8]

Lao L., 2007, STOCHASTICS, V79, P505, DOI DOI 10.1080/17442500701433509

[9] Exponential functionals of Brownian motion, I: Probability laws at fixed time [J].

Matsumoto, Hiroyuki .

PROBABILITY SURVEYS, 2005, 2 :312-347

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