There is a multidimensional process X defined via its SDE (we can assume that its a diffusion type process), and lets define another process by $g_t = E[G(X_T)|X_t]$ for $t\leq T$.
I would like to simulate process $g_t$, i.e. discretize to use in a Monte-Carlo simulation. What is the best way to do it?
The two approaches I can think of is (i) use Feynman-Kac and Finite Differeces to get $g_t$ as a function of $X$ and $t$, simulate $X_t$ and calculate $g_t$ (ii) use some form of Longstaff-Schwarz algorithm
Is there any better/simpler method?