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

View as HTML
View as gif image

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.

Location: http://mech.math.msu.su/~fpm/eng/k13/k132/k13216h.htm

Last modified: January 7, 2014