A local limit theorem for random walks in random scenery and on randomly oriented lattices
نویسندگان
چکیده
منابع مشابه
A Local Limit Theorem for Random Walks in Random Scenery and on Randomly Oriented Lattices
Random walks in random scenery are processes defined by Zn := ∑n k=1 ξX1+...+Xk , where (Xk, k ≥ 1) and (ξy, y ∈ Z) are two independent sequences of i.i.d. random variables. We assume here that their distributions belong to the normal domain of attraction of stable laws with index α ∈ (0, 2] and β ∈ (0, 2] respectively. These processes were first studied by H. Kesten and F. Spitzer, who proved ...
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When the support of X1 is a subset of N , (Sn)n≥0 is called a renewal process. Each time the random walk is said to evolve in Z, it implies that the walk is truly d-dimensional, i.e. the linear space generated by the elements in the support of X1 is d-dimensional. Institut Camille Jordan, CNRS UMR 5208, Université de Lyon, Université Lyon 1, 43, Boulevard du 11 novembre 1918, 69622 Villeurbanne...
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Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems — yielding a Gaussian density multiplied by a highly oscillatory modulating factor — for such models have been obtained. In the one-dimensional nearest-neighbor case with i.i.d. transition probabilities, local limits of uni...
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Carol Bezuidenhout and Geoffrey Grimmett Abstract. A beam of light shines through the lattice Zd, and is subjected to reflections determined by a random environment of mirrors at the vertices of Zd. The behaviour of the light ray is investigated under the hypothesis that the environment contains a strictly positive density of vertices at which the light behaves in the manner of a random walk. W...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2011
ISSN: 0091-1798
DOI: 10.1214/10-aop606