Псевдодиференціальні рівняння та альфа-стійкі випадкові процеси

Abstract

The notion of a single-layer potential for a class of pseudodifferential equations associated with rotationally invariant $\alpha$-stable stochastic processes is introduced. A certaine analogy to the classical theorem on the jump of the conormal derivative of a single-layer potential is established. This result makes it possible to construct fundamental solutions of some initial-boundary value problems for the equations mentioned above. A probabilistic interpretation of those solutions is presented. The results of investigations on the topic published by the authors during 2014--2018 are expounded in this article in a systematized and modified form.