Perturbation of an α-stable type stochastic process by a pseudo-gradient
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...
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| Format: | Article |
| Language: | English |
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2024-06-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://www.vmsta.org/doi/10.15559/24-VMSTA259 |
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| _version_ | 1841549997136412672 |
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| author | Mykola Boiko Mykhailo Osypchuk |
| author_facet | Mykola Boiko Mykhailo Osypchuk |
| author_sort | Mykola Boiko |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-474eaa83bdd743e892c5875d4aca655e |
| institution | Kabale University |
| issn | 2351-6046 2351-6054 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj-art-474eaa83bdd743e892c5875d4aca655e2025-01-10T11:16:08ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542024-06-0112112510.15559/24-VMSTA259Perturbation of an α-stable type stochastic process by a pseudo-gradientMykola Boiko0Mykhailo Osypchuk1Vasyl Stefanyk Precarpathian National University, Shevchenko 57, 76018 Ivano-Frankivsk, UkraineVasyl Stefanyk Precarpathian National University, Shevchenko 57, 76018 Ivano-Frankivsk, UkraineA 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.https://www.vmsta.org/doi/10.15559/24-VMSTA259<italic>α</italic>-stable processperturbationpseudo-gradientpseudo-process |
| spellingShingle | Mykola Boiko Mykhailo Osypchuk Perturbation of an α-stable type stochastic process by a pseudo-gradient Modern Stochastics: Theory and Applications <italic>α</italic>-stable process perturbation pseudo-gradient pseudo-process |
| title | Perturbation of an α-stable type stochastic process by a pseudo-gradient |
| title_full | Perturbation of an α-stable type stochastic process by a pseudo-gradient |
| title_fullStr | Perturbation of an α-stable type stochastic process by a pseudo-gradient |
| title_full_unstemmed | Perturbation of an α-stable type stochastic process by a pseudo-gradient |
| title_short | Perturbation of an α-stable type stochastic process by a pseudo-gradient |
| title_sort | perturbation of an α stable type stochastic process by a pseudo gradient |
| topic | <italic>α</italic>-stable process perturbation pseudo-gradient pseudo-process |
| url | https://www.vmsta.org/doi/10.15559/24-VMSTA259 |
| work_keys_str_mv | AT mykolaboiko perturbationofanastabletypestochasticprocessbyapseudogradient AT mykhailoosypchuk perturbationofanastabletypestochasticprocessbyapseudogradient |