Let be a martingale. Show that
So using the covariance formula, I know that
Now I know that I must use the property of martingale in which , but how should I mix that property in this problem? Should I take the double expectation on it? Thanks.
Let be a martingale. Show that
So using the covariance formula, I know that
Now I know that I must use the property of martingale in which , but how should I mix that property in this problem? Should I take the double expectation on it? Thanks.
Hello,
WLOG, we can suppose that i>j. Expand everything in
Then yes you have to take the double expectation for each term.
Just note that according to the martingale property for any , it would be useful to condition by the X with the lowest index.
For example, .
For , note that with the martingale property,
So that .