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Let $f$ be a continous deterministic function defined on $[0,c]$ and $(B^{H}_{t})_{t\geq 0}$ be a fBM with $H\in(0,1)$. We define a Process $ (X_{t})_{t\geq 0}$ with $X_{t}=\int_{0}^{c}f(s)B^{H}_{t+s}ds.$ Am I right, assuming, that $(X_{t})$ is centered, gaussian and stationary?

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    Correction: substitution and stationary increments of $B^{H}$.2012-09-11

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