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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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\begin{center} 
  4:15 p.m., Tuesday, June 24, 2008\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Mark Podolskij} \\
  Post.doc. at CREATES\\
  Aarhus University
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  \subsection*{  Power variation for  Gaussian processes with stationary increments }
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\noindent
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
condition on the path of the process $\phi$ we prove the convergence
in probability
for the properly normalised realised power variation. Moreover,
under a further assumption on the H\"older index of the path of $\phi$, we show
an associated stable central limit theorem. The main tool is a general
central limit theorem, due essentially to  Hu \& Nualart (2005),
Nualart \& Peccati (2005) and Peccati \& Tudor (2005),
for sequences of random variables which admit a chaos representation.

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