Expectation value of exponential of a function - first two moments of function known I have a function $f(t)$ and know that $\langle f(t)\rangle=0$ and $\langle f(t)f(t')\rangle=C(t-t')$;
Now i want to calculate:
$$\left\langle\exp\left(\int\limits_{0}^t f(t') \, \mathrm{d}t'\right)\right\rangle$$
I tried to look at the sum definition of the exponential but could do anything...
Any help?

I think what you mean is that $f$ is a stochastic process (rather than a function) of mean $0$ and covariance $C(t - t')$.  If it's a Gaussian process, that's all you need to determine it, but if it's non-Gaussian you really don't know enough to say anything about expectations of exponentials.  They might not even exist.
