Please use this identifier to cite or link to this item:
http://doi.org/10.25358/openscience-7223
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 |
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universality_for_persistence_-20221014123002935.pdf | 361.97 kB | Adobe PDF | View/Open |