Further scaling exponents of random walks in random sceneries

Abstract

Completing previous results, we construct, for every 1 2 ⩽s⩽1 , explicit examples of nearest neighbour random walks on the nonnegative integer line such that s is the scaling exponent of the associated random walk in random scenery for square integrable i.i.d. sceneries. We use coupling techniques to compare the distributions of the local times of such random walks.