Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Here is the scenario I am presented with. I am supposed to show it is a martingale:

enter image description here

Here is what I have done so far. I am fairly sure it is correct, I just don't know how to simplify it.

enter image description here

Thanks for the help.

share|cite|improve this question
It looks like you are on the right track. Here's a hint, what is $E( S_n )$ for any $n$? More importantly, if you have two r.v. X and Y and X is F_n measurable, then E(XY|F_n) = X E(Y|F_n). Notice that $S_m$ is independent of $S_{m+n}-S_m$. – Alex R. Mar 31 '12 at 23:40

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.