Abstract
We obtain sharp sufficient conditions for exponentially integrable stochastic processes , to have sample paths with bounded ‐variation. When is moreover Gaussian, we also provide a bound of the expectation of the associated ‐variation norm of . For a Hermite process of order and of Hurst index , we show that is of bounded ‐variation where , and that this is optimal. This shows that in terms of ‐variation, the Rosenblatt process (corresponding to ) has more rough sample paths than the fractional Brownian motion (corresponding to ).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
