Absolute continuity of Rosenblatt measures
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908995679158272 |
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| author | Čoupek, Petr Duncan, Tyrone E. Pasik-Duncan, Bozenna Slavík, Jakub |
| author_facet | Čoupek, Petr Duncan, Tyrone E. Pasik-Duncan, Bozenna Slavík, Jakub |
| contents | In the article, we address the problem of absolute continuity of translated Rosenblatt measures on the path space. In [Čoupek, P., Kříž, P., Maslowski, B., Stoch. Proc. Appl. 179 (2025) art. no. 104499], it is shown that there is no probability measure that would be equivalent to the original probability measure and under which a Rosenblatt path with a linear drift would again be a Rosenblatt path. Here, we show that if the Rosenblatt path is shifted in a direction belonging to a class of nontrivial Gaussian variables (that consists of a deterministic shift and a Wiener integral with respect to a fractional Brownian motion with a related Hurst parameter), such a measure exists. We also give several examples to demonstrate the scope of the result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24664 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Absolute continuity of Rosenblatt measures Čoupek, Petr Duncan, Tyrone E. Pasik-Duncan, Bozenna Slavík, Jakub Probability 60G22 In the article, we address the problem of absolute continuity of translated Rosenblatt measures on the path space. In [Čoupek, P., Kříž, P., Maslowski, B., Stoch. Proc. Appl. 179 (2025) art. no. 104499], it is shown that there is no probability measure that would be equivalent to the original probability measure and under which a Rosenblatt path with a linear drift would again be a Rosenblatt path. Here, we show that if the Rosenblatt path is shifted in a direction belonging to a class of nontrivial Gaussian variables (that consists of a deterministic shift and a Wiener integral with respect to a fractional Brownian motion with a related Hurst parameter), such a measure exists. We also give several examples to demonstrate the scope of the result. |
| title | Absolute continuity of Rosenblatt measures |
| topic | Probability 60G22 |
| url | https://arxiv.org/abs/2604.24664 |