Large deviations for local time fractional Brownian motion and applications

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dc.creatorMeerschaert, Mark M.
dc.creatorNane, Erkan
dc.creatorXiao, Yimin
dc.date2007-12-04
dc.date.accessioned2026-07-07T09:46:30Z
dc.date.available2026-07-07T09:46:30Z
dc.descriptionLet $W^H=\{W^H(t), t \in \rr\}$ be a fractional Brownian motion of Hurst index $H \in (0, 1)$ with values in $\rr$, and let $L = \{L_t, t \ge 0\}$ be the local time process at zero of a strictly stable Lévy process $X=\{X_t, t \ge 0\}$ of index $1<α\leq 2$ independent of $W^H$. The $\a$-stable local time fractional Brownian motion $Z^H=\{Z^H(t), t \ge 0\}$ is defined by $Z^H(t) = W^H(L_t)$. The process $Z^H$ is self-similar with self-similarity index $H(1 - \frac 1 α)$ and is related to the scaling limit of a continuous time random walk with heavy-tailed waiting times between jumps (\cite{coupleCTRW,limitCTRW}). However, $Z^H$ does not have stationary increments and is non-Gaussian. In this paper we establish large deviation results for the process $Z^H$. As applications we derive upper bounds for the uniform modulus of continuity and the laws of the iterated logarithm for $Z^H$.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0712.0574
dc.identifierhttp://arxiv.org/abs/0712.0574
dc.identifierJournal of Mathematical Analysis and Applications, Volume 346, Issue 2, 15 October 2008, Pages 432-445
dc.identifierdoi:10.1016/j.jmaa.2008.05.087
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163552
dc.subjectProbability
dc.subject60G18
dc.titleLarge deviations for local time fractional Brownian motion and applications
dc.typetext

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