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