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Lower tail bounds for local times of self-similar processes.

Oberseminar Darmstadt

Datum: 25.10.2018

Zeit: 16:15–17:45 Uhr

Abstract: I will demonstrate that $P(L(t)<1) ~ t^{-(1-H)}$, where $L$ is
the local time at $0$ of any recurrent $H$-self-similar real-valued
process $X$ with stationary increments that admits a sufficiently
regular local time. A special case is the Gaussian setting, i.e. when
the underlying process is fractional Brownian motion, in which the
result settles a conjecture by Molchan [Commun. Math. Phys. 205, 97-111
(1999)] who obtained the upper bound $1-H$ on the exponent.


Dr. Christian Mönch, Johannes Gutenberg-Universität Mainz


TU Darmstadt S2|15 Raum 401
Schlossgartenstr. 7, 64289 Darmstadt


Technische Universität Darmstadt

Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381


Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz

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