Possible Duplicate:
sub martingales and more
Can someone help me compute the expected value of $X_{n+1}$, that is : $E[X_{n+1}| X_0,\dots,X_n] $?
Given : $X_n = X_0 e^ {\mu S_n}$, $X_0 > 0$
where $S_n$ is a symmetric random walk and $\mu$ is greater than zero.
I am aware that the expected value of a given function is the mean. But i would like to know a method to compute the above. What is the right approach to get started on such problems on expected value computation.
Update:
I understand that $X_{n+1} = X_n \cdot e^{\mu (S_{n+1} - S_n)}$ ? How do I proceed with computing the expectation?