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Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2016

Persistence exponent for random processes in Brownian scenery

Résumé

In this paper we consider the persistence properties of random processes in Brownian scenery, which are examples of non-Markovian andnon-Gaussian processes. More precisely we study the asymptotic behaviour for large $T$, of the probability $P[ \sup_{t\in[0,T]} \Delta_t \leq 1] $where $\Delta_t = \int_{\mathbb{R}} L_t(x) \, dW(x).$Here $W={W(x); x\in\mathbb{R}}$ is a two-sided standard real Brownian motion and ${L_t(x); x\in\mathbb{R},t\geq 0}$ isthe local time of some self-similar random process $Y$, independent from the process $W$. We thus generalize the results of \cite{BFFN} where the increments of $Y$ were assumed to be independent.
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Dates et versions

hal-01017142 , version 1 (01-07-2014)
hal-01017142 , version 2 (16-02-2015)

Identifiants

Citer

Fabienne Castell, Nadine Guillotin-Plantard, Frederique Watbled. Persistence exponent for random processes in Brownian scenery. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2016, 13 (1), pp.79-94. ⟨hal-01017142v2⟩
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