We develop the asymptotic theory for the realised power variation of the processes X=[phi]-G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path of...

This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed by...

The only normal martingales which posses the chaotic representation property and the weaker predictable representation property and which are at the same time also Lévy processes, are in essence Brownian motion and the compensated Poisson process. For a general Lévy process (satisfying some...