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On the third initial-boundary value problem for some class of pseudo-differential equations related to a symmetric \(\alpha \)-stable process

  • M. M. Osypchuk
  • M. I. Portenko
Article

Abstract

A fundamental solution of the so-called third initial-boundary value problem for one class of pseudo-differential equations is constructed. Those equations are related to a symmetric \(\alpha \)-stable stochastic process and our constructions are inspired by some probabilistic ideas. However, we expound our results in a way completely independent of any probabilistic notion. Only the last section of the paper is based on the notion of a stochastic process and also a pseudo-process and it gives some interpretation of our results in terms of stochastic analysis.

Keywords

Pseudo-differential equations Initial-boundary value problem Fundamental solution Single-layer potential \(\alpha \)-Stable stochastic process 

Mathematics Subject Classification

Primary 35S11 Secondary 60G52 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of Statistics and High MathematicsVasyl Stefanyk Precarpathian National UniversityIvano-FrankivskUkraine
  2. 2.Department of Theory of Random ProcessesInstitute of Mathematics of the National Academy of Sciences of UkraineKyivUkraine

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