How can I write the following expectation $E[f(X_t,X_s)]$ by means of a Lebesgue integral and the density of $X_t$? where $f$ is a "nice" function and $X_t$ is a process without independent increments!
Is there a way to do it without using joint distributions if we know the quantity $E[(X_t-X_s)X_s]$ for $t>s$?