On the Variational Regularity of Cameron-Martin paths
- Authors: Peter K. Friz, Benjamin Gess, Sebastian Riedel
- Preprint year: 2013
- First public date: 2013-05-13
- arXiv: 1305.2943
Abstract
It is a well-known fact that finite rho-variation of the covariance (in 2D sense) of a general Gaussian process implies finite rho-variation of Cameron-Martin paths. In the special case of fractional Brownian motion (think: 2H=1/rho), in the rougher than Brownian regime, a sharper result holds thanks to a Besov-type embedding [Friz-Victoir, JFA, 2006]. In the present note we give a general result which closes this gap. We comment on the importance of this result for various applications.