$m$ -adic分析的若干问题及其对$m$ -adic随机过程的应用
Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes
摘要：
本文将$p$ -adic数域的分析推广到$m$ -adic数环的$m$情形. $p$ -adic分析的基本陈述、定理和公式可以不加修改地用于$m$-adic分析的情形。讨论了$m$ -adic数的基本性质，并考虑了$m$ -adic积分和$m$ -adic Fourier分析的一些性质.引入了无穷可分$m$ -adic分布类和$m$ -adic随机Levi过程类.研究了一类特殊的$m$ -adic CTRW过程，并将分数时间$m$ -adic随机游动作为其扩散极限.我们发现了分数时间$m$ -adic随机游动的初始分布支持度的概率测度的渐近行为。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
