Suppose I have a diffusion process
$dX_t = a(X_t)dt + b(X_t)dW_t$. Is there a straightforward method for approximating the first few moments of $X_T$ for some time $T$? Clearly, one could use Monte-Carlo methods, but I'd like something a bit more analytical.
Is it possible to use stochastic Taylor expansions to find such an estimate, for example?