An explicit form of the fundamental solution of the master equation for a jump-diffusion Ornstein-Uhlenbeck process
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913310775967744 |
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| author | Rozanova, Olga S. Krutov, Nikolai A. |
| author_facet | Rozanova, Olga S. Krutov, Nikolai A. |
| contents | An integro-differential equation for the probability density of the generalized stochastic Ornstein-Uhlenbeck process with jump diffusion is considered. It is shown that for a certain ratio between the intensity of jumps and the speed of reversion, the fundamental solution can be found explicitly. The properties of this solution are investigated. The fundamental solution allows one to obtain explicit formulas for the densities at each moment of time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_13567 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An explicit form of the fundamental solution of the master equation for a jump-diffusion Ornstein-Uhlenbeck process Rozanova, Olga S. Krutov, Nikolai A. Mathematical Physics Data Analysis, Statistics and Probability 60E05 5Q84 82C31 An integro-differential equation for the probability density of the generalized stochastic Ornstein-Uhlenbeck process with jump diffusion is considered. It is shown that for a certain ratio between the intensity of jumps and the speed of reversion, the fundamental solution can be found explicitly. The properties of this solution are investigated. The fundamental solution allows one to obtain explicit formulas for the densities at each moment of time. |
| title | An explicit form of the fundamental solution of the master equation for a jump-diffusion Ornstein-Uhlenbeck process |
| topic | Mathematical Physics Data Analysis, Statistics and Probability 60E05 5Q84 82C31 |
| url | https://arxiv.org/abs/2301.13567 |