Given the following stochastic process:
$$ dX = a(X,t)dt + b(X,t)dz $$
where:
$$ dz = A \sqrt{dt}$$
and $A$ is a random variable with mean zero and variance $1$.
Is there a way to calculate the expected value of $X$ at some time $t$? My suspection is that it is simply the integral of the expected value of $dX$. However, the function impacts its own expected value, so I could also imagine that the answer is very different. Any help here? Thanks :)