Limit theorem for random walk in weakly dependent random scenery
Nadine Guillotin-Plantard, Clémentine Prieur (2010)
Annales de l'I.H.P. Probabilités et statistiques
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Let =( )≥0 be a random walk on ℤ and =( )∈ℤ a stationary random sequence of centered random variables, independent of . We consider a random walk in random scenery that is the sequence of random variables ( )≥0, where =∑=0 , ∈ℕ. Under a weak dependence assumption on the scenery we prove a functional limit theorem generalizing Kesten and Spitzer’s [ (1979) 5–25]...