List questions from stopping-times

Published on 18 Jul 2022 - 18:49

181

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A stopping time problem for a random walk with transition probabilities dependent on states

Published on 20 Jul 2022 - 12:08

36

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Integrability of time dependent hitting times of Brownian Motion

Published on 04 Aug 2022 - 9:06

300

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Find $\mathbb{E}[N]$ for $N=\min_{n\in\mathbb{N}}\Big\{{\sum_{i=1}^{n}X_i\geq 1000}\Big\}$ if $X_i\sim U(0,1) $ i.i.d using renewal theory

Published on 13 Mar 2026 - 4:22

742

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Gambler's Ruin: Expected time of ruin using martingale and stopping time

Published on 04 Aug 2022 - 14:47

107

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Optional sampling theorem with $L^2$ bounded martingale with stopping time

Published on 07 Aug 2022 - 22:57

115

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Theorem 8.1.1 of Øksendal textbook

Published on 01 Apr 2026 - 19:08

152

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Expected stopping time in bounded random walk with unbounded steps

Published on 23 Aug 2022 - 13:38

140

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How to prove the Martingale's property if we have a special stopping time?

Published on 27 Mar 2026 - 6:12

64

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Convergence in L2 of a stopped process implies convergence in probability of the unstopped.

Published on 06 Sep 2022 - 16:57

121

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Average value from summed uniform rolls with threshold

Published on 10 Sep 2022 - 19:54

486

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Density of hitting time for a two-sided barrior for Brownian motion with drift

Published on 01 Apr 2026 - 20:49

41

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First passage time in a renewal reward process

Published on 13 Mar 2026 - 4:32

80

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Calculate the expectation of $\tau$=inf{$n\in\mathbb{N}_0|\exists{k}\lt{n}:S_{k}\le-1, S_n=1$}

Published on 24 Sep 2022 - 16:59

60

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For an increasing sequence if stopping times, $\Omega\subset\bigcup_{n \in \mathbb{N}}\{\tau_n=\tau\}$

Published on 29 Sep 2022 - 14:54

List Question

Measurability of counting processes

A stopping time problem for a random walk with transition probabilities dependent on states

Integrability of time dependent hitting times of Brownian Motion

Find $\mathbb{E}[N]$ for $N=\min_{n\in\mathbb{N}}\Big\{{\sum_{i=1}^{n}X_i\geq 1000}\Big\}$ if $X_i\sim U(0,1) $ i.i.d using renewal theory

Gambler's Ruin: Expected time of ruin using martingale and stopping time

Optional sampling theorem with $L^2$ bounded martingale with stopping time

Theorem 8.1.1 of Øksendal textbook

Expected stopping time in bounded random walk with unbounded steps

How to prove the Martingale's property if we have a special stopping time?

Convergence in L2 of a stopped process implies convergence in probability of the unstopped.

Average value from summed uniform rolls with threshold

Density of hitting time for a two-sided barrior for Brownian motion with drift

First passage time in a renewal reward process

Calculate the expectation of $\tau$=inf{$n\in\mathbb{N}_0|\exists{k}\lt{n}:S_{k}\le-1, S_n=1$}

For an increasing sequence if stopping times, $\Omega\subset\bigcup_{n \in \mathbb{N}}\{\tau_n=\tau\}$

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