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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.

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