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arXiv · 1012.1248

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

Mikhail V. Dolgopolov·Alexander P. Zubarev
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Abstract

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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Mikhail V. Dolgopolov, Alexander P. Zubarev. 2010-12-06. Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes. https://doi.org/10.1134/s2070046611010043

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