Absolute continuity of Rosenblatt measures
Abstract
In the article, we address the problem of absolute continuity of translated Rosenblatt measures on the path space. In [\v{C}oupek, P., K\v{r}\'i\v{z}, 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.
Keywords
Cite
@article{arxiv.2604.24664,
title = {Absolute continuity of Rosenblatt measures},
author = {Petr Čoupek and Tyrone E. Duncan and Bozenna Pasik-Duncan and Jakub Slavík},
journal= {arXiv preprint arXiv:2604.24664},
year = {2026}
}
Comments
14 pages