Construction of a Lévy-type process by means of the parametrix method

1Knopova, VP
2Kulik, AM
1V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
2Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2016, 5:22-29
https://doi.org/10.15407/dopovidi2016.05.022
Section: Information Science and Cybernetics
Language: Ukrainian
Abstract: 
For a wide class of integro-differential operators, it is proved that the $C_\infty({\mathbb R}^n)$-closure of each of such operators is the generator of a semigroup corresponding to a Feller Markov process. The transition probability density of the process is expressed in the form of a convergent series, and the estimates from above and below are provided. The proof is based essentially on a generalization of the parametrix method for the Cauchy problem for pseudodifferential operators.
Keywords: generator, Levi's parametrix method, Lévy-type processes, pseudodifferential operator, transition probability density
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