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Strong approximation for the general Resten-Spitzer random walk in independent random scenery

✍ Scribed by Lixin Zhang

Publisher
SP Science China Press
Year
2001
Tongue
English
Weight
502 KB
Volume
44
Category
Article
ISSN
1674-7283

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πŸ“œ SIMILAR VOLUMES

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In this note we study the strong approximation for a one-dimensional simple random walk in a general i.i.d. scenery when the scenery has only ΓΏnite lower moments. Namely, an approximation is obtained when the scenery has only ΓΏnite (2 + )th moments.

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We consider a nearest neighbor, symmetric random walk on a homogeneous, ergodic random lattice Z d . The jump rates of the walk are independent, identically Bernoulli distributed random variables indexed by the bonds of the lattice. A standard result from the homogenization theory, see [A. De Masi,