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| Format: | Preprint |
| Published: |
2022
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| Online Access: | https://arxiv.org/abs/2206.11798 |
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| _version_ | 1866913581530873856 |
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| author | Szabłowski, Paweł J. |
| author_facet | Szabłowski, Paweł J. |
| contents | We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not have to care about the distribution of their jumps which is always difficult to find. Among them are the Ornstein-Uhlenbeck process, the Gamma process, the process with Arcsin margins and the Theta function transition densities and others. We give a simple criterion for the stationary process to have a continuous path modification expressed in terms of skewness and excess kurtosis of the marginal distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_11798 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths Szabłowski, Paweł J. Probability Analysis of PDEs Primary 60G10, 60G17 Secondary 60J35, 60G44 We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not have to care about the distribution of their jumps which is always difficult to find. Among them are the Ornstein-Uhlenbeck process, the Gamma process, the process with Arcsin margins and the Theta function transition densities and others. We give a simple criterion for the stationary process to have a continuous path modification expressed in terms of skewness and excess kurtosis of the marginal distribution. |
| title | Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths |
| topic | Probability Analysis of PDEs Primary 60G10, 60G17 Secondary 60J35, 60G44 |
| url | https://arxiv.org/abs/2206.11798 |