Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/5868
Title: On some perturbatіons of a stable process and solutіons to the Cauchy problem for a class of pseudo-dіfferentіal equatіons
Authors: Osypchuk, Mykhailo
Keywords: stable process
Cauchy problem
pseudo-differential equation
transition probability density
Issue Date: Jun-2015
Citation: Osypchuk M.M. On some perturbatіons of a stable process and solutіons to the Cauchy problem for a class of pseudo-dіfferentіal equatіons/ M.M. Osypchuk// Carpathіan Math. Publ. -2015. -V. 7, 1. -P. 101–107.
Abstract: A fundamental solution of some class of pseudo-differential equations is constructed by a method based on the theory of perturbations. We consider a symmetric α-stable process in multidimensional Euclidean space. Its generator A is a pseudo-differential operator whose symbol is given by − c | λ | α , where the constants α ∈ ( 1, 2 ) and c > 0 are fixed. The vector-valued operator B has the symbol 2ic | λ | α − 2 λ. We construct a fundamental solution of the equation u t = ( A + ( a (·) , B )) u with a continuous bounded vector-valued function a.
URI: http://hdl.handle.net/123456789/5868
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