Translator Disclaimer
June 2012 Fractional relaxation equations and Brownian crossing probabilities of a random boundary
L. Beghin
Author Affiliations +
Adv. in Appl. Probab. 44(2): 479-505 (June 2012). DOI: 10.1239/aap/1339878721

Abstract

In this paper we analyze different forms of fractional relaxation equations of order ν ∈ (0, 1), and we derive their solutions in both analytical and probabilistic forms. In particular, we show that these solutions can be expressed as random boundary crossing probabilities of various types of stochastic process, which are all related to the Brownian motion $B$. In the special case ν = ½, the fractional relaxation is shown to coincide with Pr{sup0≤stB(s) < U} for an exponential boundary U. When we generalize the distributions of the random boundary, passing from the exponential to the gamma density, we obtain more and more complicated fractional equations.

Citation

Download Citation

L. Beghin. "Fractional relaxation equations and Brownian crossing probabilities of a random boundary." Adv. in Appl. Probab. 44 (2) 479 - 505, June 2012. https://doi.org/10.1239/aap/1339878721

Information

Published: June 2012
First available in Project Euclid: 16 June 2012

zbMATH: 1251.60032
MathSciNet: MR2977405
Digital Object Identifier: 10.1239/aap/1339878721

Subjects:
Primary: 33E12, 34A08, 60G15

Rights: Copyright © 2012 Applied Probability Trust

JOURNAL ARTICLE
27 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.44 • No. 2 • June 2012
Back to Top