solve for stochastic partial differential equation dS(t)=sigma(S(t))dW(t), S(t)=0 by un-Monte Carlo

Hi Is anyone have some experience of dealing with the follow: dS(t)=sigma(S(t))dW(t) S(t)=s0 where sigma could be any function in terms of S(t), W(t) is Brownian Motion. I am only interested in E(g(t)),where g(S(t))is again a arbitrary function, not the process S(t) itself. The obvious way is using Monte Carlo simulation. But I am wondering if there is any other typical method. Thank you!