In some projects I got to a conditional expectation of the form:
where $t\geq s$, $f$ is nice enough and $X$ is an Ito process and $\mathcal F_s$ is the information about $X$ up to time $s$. I want to compute this. Is there anyway to do so?
I tried Taylor expanding $\exp$, I tried to apply Ito formula in a few clever ways and nothing works out nicely. Is there anyway of computing this?