I want to calculate the following:
$E(\sqrt{f(x(t))})$, where $E$ denotes the expectation value.
$f$ is some function,
$x(t)$ is my stochastic process,
and i know that $\left\langle x(t)\right\rangle=0$,
$\left\langle x(t')x(t'')\right\rangle=g(t'-t'')$ and
$\left\langle x(t_1)x(t_2)...x(t_n)\right\rangle=0$ for $n \ge 3$.
My guess would be to expand the root with a taylor expansion? Is there an easier way?