Relaxation equations with stretched non-local operators: renewal and time-changed processes

Beghin, Luisa, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Vaz, Jayme 2025. Relaxation equations with stretched non-local operators: renewal and time-changed processes. Journal of Theoretical Probability Item availability restricted.

	PDF - Accepted Post-Print Version Restricted to Repository staff only Download (582kB)
	PDF (Provisional File) - Accepted Post-Print Version Download (17kB)

Abstract

We introduce and study renewal processes defined by means of extensions of the standard relaxation equation through “stretched” non-local operators (of order α and with parameter γ). In a first case we obtain a generalization of the fractional Poisson process, which displays either infinite or finite expected waiting times between arrivals, depending on the parameter γ. Therefore, the introduction in the operator of the non-homogeneous term driven by γ allows us to regulate the transition between different regimes of our renewal process. We then consider a second-order relaxation-type equation involving the same operator, under different sets of conditions on the constants involved; for a particular choice of these constants, we prove that the corresponding renewal process is linked to the first one by convex combination of its distributions. We also discuss alternative models related to the same equations and their time-changed representation, in terms of the inverse of a non-decreasing process which generalizes the α-stable Levy subordinator

Item Type:	Article
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	Springer
ISSN:	0894-9840
Date of First Compliant Deposit:	9 December 2025
Date of Acceptance:	30 November 2025
Last Modified:	10 Dec 2025 11:00
URI:	https://orca.cardiff.ac.uk/id/eprint/183068

Actions (repository staff only)

Edit Item