Perturbation of an α -stable type stochastic process by a pseudo-gradient
Pub. online: 25 June 2024
Type: Research Article
Open Access
Open Access
Received
25 June 2023
25 June 2023
Revised
18 May 2024
18 May 2024
Accepted
25 May 2024
25 May 2024
Published
25 June 2024
25 June 2024
Abstract
A Markov process defined by some pseudo-differential operator of an order $1\lt \alpha \lt 2$ as the process generator is considered. Using a pseudo-gradient operator, that is, the operator defined by the symbol $i\lambda |\lambda {|^{\beta -1}}$ with some $0\lt \beta \lt 1$, 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.
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