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expected value of a function
Can someone help me compute the expected value of $X_{n+1}$, that is : $E[X_{n+1}\mid X_0,X_1,\ldots,X_{n+1}]$, given : $X_n = X_0 e^{\mu \cdot S_n}$, $X_0 > 0$, 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.
So I understand that $X_{n+1} = X_n e^{\mu \cdot (S_{n+1} - S_n)}$ ? How do I proceed with computing the expectation?