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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

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 ∈ 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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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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Keywords

  • Random Walk
  • Transition Function
  • Energy Landscape
  • Cayley Tree
  • Ultrametric Space