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Potential Analysis

, Volume 28, Issue 2, pp 185–200 | Cite as

Parabolic Equations and Markov Processes Over p-Adic Fields

  • W. A. Zúñiga-Galindo
Article

Abstract

In this paper we construct and study a fundamental solution of Cauchy’s problem for p-adic parabolic equations of the type
$$\frac{\partial u\left( x,t\right) }{\partial t}+\left( f\left( D,\beta\right) u\right) \left( x,t\right) =0,x\in \mathbb{Q}_{p}^{n},n\geq 1,t\in\left( 0,T\right] ,$$
where \(f\left( D,\beta \right) , \beta >0\), is an elliptic pseudo-differential operator. We also show that the fundamental solution is the transition density of a Markov process with state space \(\mathbb{Q}_p^n \).

Keywords

Parabolic equations Ultrametric difussion Pseudo-differential operators Markov processes p-adic fields 

Mathematics Subject Classifications (2000)

Primary 35K30; Secondary 46S10 

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Departamento de MatemáticasCentro de Investigación y de Estudios Avanzados del I.P.N.México D.F.México
  2. 2.Department of Mathematics and Computer ScienceBarry UniversityMiami ShoresUSA

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