ON THE QUENCHED FUNCTIONAL CLT IN RANDOM SCENERIES

In this section we repeatedly apply Lemma 3.1 and Corollary 3.3 to reduce the problem of finding weak quenched limits of the hitting times T n to the problem of finding weak

We prove a level 3 large deviation principle, under almost every environment, with rate function related to a relative

In Section 3 a sequence of random measures is associated with the random scenery and con- ditions to ensure its convergence to a stable, Gaussian or fractional Gaussian random noise

Keywords : Random walk in random scenery; Weak limit theorem; Law of the iterated logarithm; Brownian motion in Brownian Scenery; Strong approxima- tion.. AMS Subject Classification

As X 1 , Y 1 are two independent Gaussian random variables, the second term in the upper bound has exponential moments by Fact 2.5.. The same arguments will directly apply to prove

Motivated by random evolutions which do not start from equilibrium, in a recent work, Peligrad and Voln´ y (2018) showed that the central limit theorem (CLT) holds for

We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random eld (r.f.) along a 2d-random walk in dierent situations: when the r.f.. is iid with

The proof of the main theorem in this paper is based upon the use of a martingale-coboundary decom- position that can be found in [32] (some more recent and general results can be