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Ultrametric Diffusion, Exponential Landscapes, and the First Passage Time Problem

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Abstract

In this article we study certain ultradiffusion equations connected with energy landscapes of exponential type. These equations are connected with the \(p\)-adic models of complex systems introduced by Avetisov et al. We show that the fundamental solutions of these equations are transition density functions of Lévy processes with state space \(\mathbb{Q}_{p}^{n}\), we also study some aspects of these processes including the first passage time problem.

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Authors and Affiliations

  1. Departamento de Matemáticas y Estádistica, Universidad del Norte, Km.5 Via Puerto Colombia, Barranquilla, Colombia

    Anselmo Torresblanca-Badillo

  2. Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional Departamento de Matemáticas, Unidad Querétaro Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Santiago de Querétaro, Qro., 76230, Mexico

    W. A. Zúñiga-Galindo

Authors
  1. Anselmo Torresblanca-Badillo
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  2. W. A. Zúñiga-Galindo
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Correspondence to W. A. Zúñiga-Galindo.

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The second author was partially supported by Conacyt Grant No. 250845

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Torresblanca-Badillo, A., Zúñiga-Galindo, W.A. Ultrametric Diffusion, Exponential Landscapes, and the First Passage Time Problem. Acta Appl Math 157, 93–116 (2018). https://doi.org/10.1007/s10440-018-0165-2

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