We develop the asymptotic theory for the realised power variation of the processes X = f • 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 condition on the path of...

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...

We present some new asymptotic results for functionals of higher order differences of Brownian semi-stationary processes. In an earlier work we have derived a similar asymptotic theory for first order differences. However, the central limit theorems were valid only for certain values of the...

In this paper we study the asymptotic behaviour of power and multipower variations of stochatstic processes. Processes of the type considered serve in particular, to analyse data of velocity increments of a uid in a turbulence regime with spot intermittency sigma. The purpose of the present...

In this paper we consider an insider with privileged information that is affected by an independent noise vanishing as the revelation time approaches. At this time, information is available to every trader. Our financial markets are based on Wiener space. In probabilistic terms we obtain an...