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First passage times for some classes of fractional time-changed diffusions

Leonenko, Nikolai and Pirozzi, Enrica 2021. First passage times for some classes of fractional time-changed diffusions. Stochastic Analysis and Applications 10.1080/07362994.2021.1953386
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Abstract

We consider some time-changed diffusion processes obtained by applying the Doob transformation rule to a time-changed Brownian motion. The time-change is obtained via the inverse of an α-stable subordinator. These processes are specified in terms of time-changed Gauss-Markov processes and fractional time-changed diffusions. A fractional pseudo-Fokker-Planck equation for such processes is given. We investigate their first passage time densities providing a generalized integral equation they satisfy and some transformation rules. First passage time densities for time-changed Brownian motion and Ornstein-Uhlenbeck processes are provided in several forms. Connections with closed form results and numerical evaluations through the level zero are given.

Item Type: Article
Date Type: Published Online
Status: In Press
Schools: Mathematics
Publisher: Taylor and Francis
ISSN: 0736-2994
Date of First Compliant Deposit: 2 August 2021
Date of Acceptance: 3 July 2021
Last Modified: 06 Oct 2021 18:27
URI: http://orca.cardiff.ac.uk/id/eprint/143088

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