Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes

Details Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes

2010-12-06

arxiv.org/abs/1012.1248v2

p-Adic Numbers, Ultrametric Analysis and Applications, 2011, Vol. 3, No. 1, pp. 39-51

Physics

Mathematical Physics

18 pages

Scientific paper

10.1134/S2070046611010043

In this paper we consider a generalization of analysis on $p$-adic numbers field to the $m$ case of $m$-adic numbers ring. The basic statements, theorems and formulas of $p$-adic analysis can be used for the case of $m$-adic analysis without changing. We discuss basic properties of $m$-adic numbers and consider some properties of $m$-adic integration and $m$-adic Fourier analysis. The class of infinitely divisible $m$-adic distributions and the class of $m$-adic stochastic Levi processes were introduced. The special class of $m$-adic CTRW process and fractional-time $m$-adic random walk as the diffusive limit of it is considered. We found the asymptotic behavior of the probability measure of initial distribution support for fractional-time $m$-adic random walk.

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