List questions from stopping-times

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Analytical solutions to $E[f(X_\tau) e^{-\alpha\tau}]$

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Show $\mathbb{E}_1\big[S_n\textbf{1}_{\{T_{\text{hit zero}} > n\}}\big] \not\to 0$ for SSRW.

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$\{\omega \ge \tau\} \in \mathscr{F}_{\tau -}$ for stopping times

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Is the supremum of a right continuous process right continuous? Defining a stopping time as the first hitting time of a supremum process

Published on 18 Jan 2022 - 13:49

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Published on 25 Jan 2022 - 12:22

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An expected increasing stochastic will stop if exceeding a threshold. What's the stopping time?

Published on 27 Jan 2022 - 14:07

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Optimal stopping of $\mathbb{E}\frac{|B_{\tau}|}{1+\tau}$

Published on 29 Jan 2022 - 23:22

List Question

Is it true $P(\sup_{k \in \mathbb{N}}X_k \geq \epsilon +x)=\dfrac{x}{\epsilon+x}$?

Analytical solutions to $E[f(X_\tau) e^{-\alpha\tau}]$

Possible example of stopped martingale not being in $L^1$

Stopping times and convergence of indexes

Show $\mathbb{E}_1\big[S_n\textbf{1}_{\{T_{\text{hit zero}} > n\}}\big] \not\to 0$ for SSRW.

Martingale and finite stopping time

Trouble with extending Doob's Optional Stopping Theorem

Why can we use limit inferior to calculate the expected value of a stopped process?

Understanding proof of discrete optimal sampling theorem

$\{\omega \ge \tau\} \in \mathscr{F}_{\tau -}$ for stopping times

Is the supremum of a right continuous process right continuous? Defining a stopping time as the first hitting time of a supremum process

Measurability of a random variable w.r.t a $\sigma$ algebra

gambler's ruin expected stopping time

An expected increasing stochastic will stop if exceeding a threshold. What's the stopping time?

Optimal stopping of $\mathbb{E}\frac{|B_{\tau}|}{1+\tau}$

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