New classes of parabolic pseudo-differential equations, Feller semigroups, contraction semigroups and stochastic process on the p-adic numbers

Author:

Torresblanca-Badillo Anselmo,Narváez Alfredo R. R.,López-González José

Abstract

AbstractTwo types of p-adic pseudo-differential operators (denoted, respectively, by $${\mathcal {T}}_{{\varvec{f}}_{1},{\varvec{f}}_{2}}^{l}$$ T f 1 , f 2 l and $${\mathcal {J}}_{{\varvec{f}}_{1},{\varvec{f}}_{2}}^{\alpha }$$ J f 1 , f 2 α ) are introduced in this article. We will show that the operator $${\mathcal {T}}_{{\varvec{f}}_{1},{\varvec{f}}_{2}}^{l}$$ T f 1 , f 2 l determines certain Feller semigroups and stochastic processes with state space the p-adic numbers. The second type of these operators (defined on a new class of p-adic Sobolev space) are connected with contraction semigroups and parabolic pseudo-differential equations.

Funder

Uninorte

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Analysis

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