List questions from stopping-times | MathQA

If $T_1, T_2$ are stopping times such that $T_1 \le T_2$ almost surely, then $\mathcal{F}_{T_1} \subset \mathcal{F}_{T_2}$

Published on 16 Jan 2023 - 18:08

How the author obtains $A \cap \{\tau_2 \leqslant t\}=A \cap\left\{\tau_1 \leqslant t\right\} \cap\left\{\tau_2 \leqslant t\right\}$?

Published on 16 Jan 2023 - 19:51

Expectation of the stopping time for certain random walk

Published on 18 Jan 2023 - 16:23

How can I show that the stopping time $T=\min\{n\geq 0: S_n=1\}<\infty$?

Published on 20 Jan 2023 - 10:38

Are $U:= \min\{n \geq 5 : S_n = S_{n-5} + 5\}$ and $V:=U-5$ stopping times for a random walk $S_n$?

Published on 22 Jan 2023 - 18:35

The stopped process $(M'_n, n \in \mathbb{N})$ with $M'_n := M_{T \wedge n}$ is a martingale

Published on 23 Jan 2023 - 11:40

How $M_T$ is well-define in this statement of optional stopping theorem?

Published on 23 Jan 2023 - 16:00

stopping time for simple symmetric random walk

Published on 25 Jan 2023 - 3:43

Showing that a stopping time is finite for an unbalanced betting game

Published on 25 Jan 2023 - 14:17

Bounding the variance of a stopping time

Published on 27 Jan 2023 - 19:36