Persistence exponent for random processes in Brownian scenery

2014/07/01 by Castell, Fabienne, Guillotin-Plantard, Nadine, Watbled, Frederique
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1407.0364

Abstract

In this paper we consider the persistence properties of random processes in Brownian scenery, which are examples of non-Markovian and non-Gaussian processes. More precisely we study the asymptotic behaviour for large T, of the probability P[ sup_t∈[0,T] Δ_t ≤ 1] where Δ_t = ∫_ℝ L_t(x) dW(x). Here W=W(x); x∈ℝ is a two-sided standard real Brownian motion and L_t(x); x∈ℝ,t≥ 0 is the local time of some self-similar random process Y, independent from the process W. We thus generalize the results of \citeBFFN where the increments of Y were assumed to be independent.

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