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arXiv · 1305.2943

On the Variational Regularity of Cameron-Martin paths

Peter K. Friz·Benjamin Gess·Sebastian Riedel
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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.

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Peter K. Friz, Benjamin Gess, Sebastian Riedel. 2013-10-31. On the Variational Regularity of Cameron-Martin paths. https://arxiv.org/abs/1305.2943

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