On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations

Abstract

A fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric α-stable process in multidimensional Euclidean space. Its generator A is a pseudo-differential operator whose symbol is given by −c|λ|α, were the constants α∈(1,2) and c>0 are fixed. The vector-valued operator B has the symbol 2ic|λ|α−2λ. We construct a fundamental solution of the equation ut=(A+(a(⋅),B))u with a continuous bounded vector-valued function a.

Authors and Affiliations

M. M. Osypchuk

Keywords

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  • EP ID EP539260
  • DOI 10.15330/cmp.7.1.101-107
  • Views 59
  • Downloads 0

How To Cite

M. M. Osypchuk (2015). On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations. Карпатські математичні публікації, 7(1), 101-107. https://europub.co.uk/articles/-A-539260