2010/02/09 by Fabienne Castell, Nadine Guillotin-Plantard, Castell, Fabienne +6
Decision Sciences · Mathematics · #60F05 #60G52 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR #msc:60F05 #msc:60G52
paper · pdf · doi:10.48550/arxiv.1002.1878
arxiv created 2010/02/09 · openalex publication_date 2010/02/09 · arxiv updated 2010/02/26 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Random walks in random scenery are processes defined by\nZn:=\∑k=1n\ξX1+...+Xk, where (Xk,k\≥ 1) and\n(\ξy,y\∈ mathbb Z) are two independent sequences of i.i.d. random\nvariables. We assume here that their distributions belong to the normal domain\nof attraction of stable laws with index \α\∈ (0,2] and \β\∈ (0,2]\nrespectively. These processes were first studied by H. Kesten and F. Spitzer,\nwho proved the convergence in distribution when \α\≠ 1 and as n\→\n\∞, of n-\δZn, for some suitable \δ>0 depending on\n\α and \β. Here we are interested in the convergence, as n\→\n\∞, of n^\δ mathbb P(Zn= lfloor n\δ x rfloor), when x\∈\n RR is fixed. We also consider the case of random walks on randomly oriented\nlattices for which we obtain similar results.\n