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arXiv · 2306.15435

Perturbation of an alpha-stable type stochastic process by a pseudo-gradient

Mykola Boiko·Mykhailo Osypchuk
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Abstract

We consider the Markov process defined by some pseudo-differential operator of the order $1<α<2$ as the process generator. Using a pseudo-gradient operator, that is, the operator defined by the symbol $iλ|λ|^{β-1}$ with some $0<β<α$, the perturbation of the Markov process by the pseudo-gradient with a multiplier integrable at some great enough power is constructed. Such perturbation defines a family of evolution operators, the properties of which are investigated.

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Mykola Boiko, Mykhailo Osypchuk. 2024-02-05. Perturbation of an alpha-stable type stochastic process by a pseudo-gradient. https://arxiv.org/abs/2306.15435

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