On the Relation between Different Constructions of Random Walks on p-adics

#### S. Albeverio, X. Zhao

2000, v.6, Issue 2, 239-255

ABSTRACT

We identify the class of random walks on $p$-adics constructed by Albeverio and Karwowski with the spherically symmetric Levy processes on $p$-adics introduced by Evans. This class naturally contains the random walks introduced by Vladimirov. We also obtain limit results on stable random walks on $p$-adics. For random walks associated with a sequence of positive decreasing numbers, we give explicit formulas for the Hausdorff and packing dimensions of their sample paths, extending Evans' results in this direction.

Keywords: random walks,Levy processes,$p$-adic spaces,Fourier transform,asymptoticbehavior,Hausdorff and packing dimensions