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A Method for Solving the p-Adic Kolmogorov–Feller Equation for an Ultrametric Random Walk in an Axially Symmetric External Field

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Abstract

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 ∈ ℚ p , of the process under consideration is nonsymmetric and depends on the norm of p-adic arguments. It is proved for transition functions of the form w(y | x) = ρ(|x − y| p )φ(|x| p ) that solving the p-adic Kolmogorov–Feller equation for a random walk in a p-adic ball of radius p R reduces to solving a system of R +1 ordinary differential equations.

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Authors and Affiliations

  1. Lomonosov Moscow State University, 119991, Moscow, Russia

    O. M. Sizova

  2. Semenov Institute of Chemical Physics of the Russian Academy of Sciences, 119991, Moscow, Russia

    O. M. Sizova

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  1. O. M. Sizova
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Correspondence to O. M. Sizova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 197–207, 2013.

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Sizova, O.M. A Method for Solving the p-Adic Kolmogorov–Feller Equation for an Ultrametric Random Walk in an Axially Symmetric External Field. J Math Sci 203, 884–891 (2014). https://doi.org/10.1007/s10958-014-2180-9

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  • DOI: https://doi.org/10.1007/s10958-014-2180-9

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