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

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Pirozzi, Enrica 2022. First passage times for some classes of fractional time-changed diffusions. Stochastic Analysis and Applications 40 (4) , pp. 735-763. 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:	Publication
Status:	Published
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:	29 Nov 2024 16:15
URI:	https://orca.cardiff.ac.uk/id/eprint/143088

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