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arXiv · 1308.5013

Nonlocal Operators, Parabolic-type Equations, and Ultrametric Random Walks

L. F. Chacón-Cortes·W. A. Zúñiga-Galindo
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Abstract

In this article we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov et al. The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.

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L. F. Chacón-Cortes, W. A. Zúñiga-Galindo. 2013-08-22. Nonlocal Operators, Parabolic-type Equations, and Ultrametric Random Walks. https://doi.org/10.1063/1.4828857

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