1
vote
0answers
52 views

Conditions for Martingale

Let $X{}_{1},X_{2},\ldots$be a sequence of independent RV and let $f{}_{j}$be continuous functions. Let $S{}_{0}=1$ and $S{}_{n}=\sum_{j=1}^{n}f_{j}\left(X_{j}\right)$. Find a necessary and sufficient ...
0
votes
1answer
69 views

Exercise-martingale-inequalities

I have another question about an exercise on martingales. I completely solved it, up to the las point, I know how the method in order to prove the last point, but I am not capable of doing it... ...
2
votes
1answer
201 views

Unbounded stopping times and optional stopping theorem

Given that ${X_n}$ is a submartingale with $\left|X_{k}-X_{k-1}\right|\leq M<\infty$, and defining stopping times $\tau_{1}<\tau_{2}$ with $E(\tau_{2})<\infty$, eventually I want to show ...