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A parametrix construction for the fundamental solution of the evolution equation associated with a pseudo-differential operator generating a Markov process. (English) Zbl 1081.35168
Author’s abstract: We use the method proposed by H. Kumano-go in the classical case to construct a parametrix of the equation \(\frac{\partial u}{\partial t}+ q (x, D )u = 0\) 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.

35S10 Initial value problems for PDEs with pseudodifferential operators
60J35 Transition functions, generators and resolvents
47D07 Markov semigroups and applications to diffusion processes
Full Text: DOI
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