期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2016
卷号：XIII
页码：79-94
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：In this paper we consider the persistence properties of random processesin Brownian scenery, which are examples of non-Markovian and non-Gaussian processes.More precisely we study the asymptotic behaviour for large T, of the probabilityP[supt2[0;T ] t 1] where t =RR Lt(x)dW(x): Here W = fW(x); x 2 Rgis a two-sided standard real Brownian motion and fLt(x); x 2 R; t 0g is the localtime of some self-similar random process Y , independent from the process W. Wethus generalize the results of Castell et al. (2013) where the increments of Y wereassumed to be independent.
