FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2013, VOLUME 18, NUMBER 2, PAGES 197-207

A method for solving the $p$-adic Kolmogorov--Feller equation for an ultrametric random walk in an axially symmetric external field

O. M. Sizova

Abstract

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A method for solving the Kolmogorov--Feller equation for an ultrametric random walk in an axially symmetric external field is considered. The transition function $w(y|x)$, $x,y$Î Q_p, of the process under consideration is nonsymmetric and depends on the norm of $p$-adic arguments. It is proved for the transition functions of the form $w(y|x)\; =$r(|x - y|_p) f(|x|_p) that solving the $p$-adic Kolmogorov--Feller equation for a random walk in a $p$-adic ball of radius $pR$ reduces to solving a system of $R+1$ ordinary differential equations.

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Last modified: January 7, 2014