Perturbation of an α-stable type stochastic process by a pseudo-gradient - Mykola Boiko; Mykhailo Osypchuk (Modern Stochastics: Theory and Applications)
A Markov process defined by some pseudo-differential operator of an order $1\lt α \lt 2$ as the process generator is considered. Using a pseudo-gradient operator, that is, the operator defined by the symbol $iλ |λ {|^{β -1}}$ with some $0\lt β \lt 1$, the perturbation of the Markov process under consideration by the pseudo-gradient with a multiplier, which is integrable at some large enough power, is constructed. Such perturbation defines a family of evolution operators, properties of which are investigated. A corresponding Cauchy problem is considered.