Authors:	Mönch, Christian
Title:	Universality for persistence exponents of local times of self-similar processes with stationary increments
Online publication date:	14-Oct-2022
Year of first publication:	2021
Language:	english
Abstract:	We show that P(ℓX(0,T]≤1)=(cX+o(1))T−(1−H), where ℓX is the local time measure at 0 of any recurrent H-self-similar real-valued process X with stationary increments that admits a sufficiently regular local time and cX is some constant depending only on X. A special case is the Gaussian setting, i.e. when the underlying process is fractional Brownian motion, in which our result settles a conjecture by Molchan [Commun. Math. Phys. 205, 97-111 (1999)] who obtained the upper bound 1−H on the decay exponent of P(ℓX(0,T]≤1). Our approach establishes a new connection between persistence probabilities and Palm theory for self-similar random measures, thereby providing a general framework which extends far beyond the Gaussian case.
DDC:	510 Mathematik 510 Mathematics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-7223
Version:	Published version
Publication type:	Zeitschriftenaufsatz
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Journal:	Journal of theoretical probability 35
Pages or article number:	1842 1862
Publisher:	Springer Science + Business Media B.V.
Publisher place:	New York, NY u.a.
Issue date:	2021
ISSN:	1572-9230
Publisher DOI:	10.1007/s10959-021-01102-8
Appears in collections:	JGU-Publikationen