Originally Posted by

**tossifan** In many books, a martingale (roughly speaking) is defined as a process X1,X2,... satisfying:

$\displaystyle

\mathbb{E}[X_{t_{n+1}} | X_{t_n},\ldots,X_{t_0}] = X_{t_n}

$

which is equivalent to

$\displaystyle

\mathbb{E}[X_{t_{n+1}} - X_{t_n} | X_{t_n},\ldots,X_{t_0}] = 0

$

While the latter is understandable to me, I interpret the former in this sense: "expectation is equal to a random variable", which is absurd to me.

Now, I am sure this is a stupid question but: how should I interpret the former?

Maybe that X_tn is no more a random variable but a number (because at time tn is known)? If so, why don't textbook put that symbol in lower case as usual... ?