A parametrix construction for the fundamental solution of the evolution equation associated with a pseudo‐differential operator generating a Markov process

Abstract

Abstract We use the method proposed by H. Kumano‐go in the classical case to construct a parametrix of the equation $ \textstyle {{\partial u} \over {\partial t}}$ + q ( x, D ) u = 0 where q ( x, D ) is a pseudo‐differential operator with symbol in the class introduced by W. Hoh. In case where – q ( x, D ) extends to a generator of a Feller semigroup our construction yields an approximation for the transition densities of the corresponding Markov process. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)