Construction of a L´evy-type process by means of the parametrix method - Knopova, V.P.; Kulik, A. M. (Reports of the National Academy of Sciences of Ukraine, 2016)
For a wide class of integro-differential operators, it is proved that the C∞(Rn)-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.