Perturbation of an alpha-stable type stochastic process by a pseudo-gradient
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929233501093888 |
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| author | Boiko, Mykola Osypchuk, Mykhailo |
| author_facet | Boiko, Mykola Osypchuk, Mykhailo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15435 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Perturbation of an alpha-stable type stochastic process by a pseudo-gradient Boiko, Mykola Osypchuk, Mykhailo Probability 60G52 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. |
| title | Perturbation of an alpha-stable type stochastic process by a pseudo-gradient |
| topic | Probability 60G52 |
| url | https://arxiv.org/abs/2306.15435 |