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Urn Problem: randomly pick a ball and replace the ball with different colour

score 125 · Answer 1 · 2026-04-15 09:46:45

125

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Urn Problem: randomly pick a ball and replace the ball with different colour

Published on 15 Apr 2026 - 9:46

score 228 · Answer 2 · 2026-03-25 12:48:42

228

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Gambler's Ruin Problem: when Smith can never be broke

Published on 25 Mar 2026 - 12:48

score 49 · Answer 3 · 2026-04-16 15:25:44

Let $\{ X^{\tau_n} \}$ be a sequence continuous stopped process. Does $E[X_t^{\tau_n}]<C$ for all $n \in \mathbb N$ imply that $E[X_t]<C$?

score 81 · Answer 4 · 2026-04-07 16:15:55

81

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Three Approaches to a Markov Chain Calculation with Three Different Answers

Published on 07 Apr 2026 - 16:15

score 221 · Answer 5 · 2026-04-16 05:27:23

A submartingale $(X_n)$ with respect to its natural filtration $(\mathcal G_n)$ where $\mathcal{G}_{n}:=\sigma (X_{0}, \ldots, X_{n})$

score 45 · Answer 6 · 2026-04-16 07:44:58

45

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Is the condition "if $\phi\left(X_{n}\right)$ is integrable" redundant in this proposition?

Published on 16 Apr 2026 - 7:44

score 43 · Answer 7 · 2026-03-26 13:02:16

43

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Calculation of the first time when a certain number of customers received service.

Published on 26 Mar 2026 - 13:02

score 1.5k · Answer 8 · 2026-04-16 12:03:55

1.5k

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Uniformly integrable martingale and $L^1$ convergence

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score 147 · Answer 9 · 2026-04-11 16:08:48

147

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Expected Total Discounted Reward

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score 444 · Answer 10 · 2026-04-13 20:11:58

444

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Is the expected distance between events in a spatial Poisson Process the same as the expected value from any point to the nearest event?

Published on 13 Apr 2026 - 20:11

score 26 · Answer 11 · 2026-04-16 21:02:34

26

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Show that $(U_{n})_{n \leq N}$ is the smallest $\mathcal{F}_{n}$-super-martingale that dominates $X_{n}$

Published on 16 Apr 2026 - 21:02

score 34 · Answer 12 · 2026-04-16 12:46:53

34

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Show that $(V_{n})_{n \le N}$ is a $\mathcal{F}_n$-martingale

Published on 16 Apr 2026 - 12:46

score 37 · Answer 13 · 2026-04-17 06:27:25

37

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Show that $(M_{n})$ with $M_{n}=(X_{n}-\mathbb{E}(X_{n}))^{2}-\operatorname{Var}(X_{n})$ is a $\mathcal{F}_{n}$-martingale

Published on 17 Apr 2026 - 6:27

score 52 · Answer 14 · 2026-04-12 14:37:16

52

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Clarification on equality of two sigma algebras

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score 73 · Answer 15 · 2026-04-13 18:47:52

73

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Sigma algebra generated by random variables

Published on 13 Apr 2026 - 18:47

List Question

Urn Problem: randomly pick a ball and replace the ball with different colour

Gambler's Ruin Problem: when Smith can never be broke

Let $\{ X^{\tau_n} \}$ be a sequence continuous stopped process. Does $E[X_t^{\tau_n}]<C$ for all $n \in \mathbb N$ imply that $E[X_t]<C$?

Three Approaches to a Markov Chain Calculation with Three Different Answers

A submartingale $(X_n)$ with respect to its natural filtration $(\mathcal G_n)$ where $\mathcal{G}_{n}:=\sigma (X_{0}, \ldots, X_{n})$

Is the condition "if $\phi\left(X_{n}\right)$ is integrable" redundant in this proposition?

Calculation of the first time when a certain number of customers received service.

Uniformly integrable martingale and $L^1$ convergence

Expected Total Discounted Reward

Is the expected distance between events in a spatial Poisson Process the same as the expected value from any point to the nearest event?

Show that $(U_{n})_{n \leq N}$ is the smallest $\mathcal{F}_{n}$-super-martingale that dominates $X_{n}$

Show that $(V_{n})_{n \le N}$ is a $\mathcal{F}_n$-martingale

Show that $(M_{n})$ with $M_{n}=(X_{n}-\mathbb{E}(X_{n}))^{2}-\operatorname{Var}(X_{n})$ is a $\mathcal{F}_{n}$-martingale

Clarification on equality of two sigma algebras

Sigma algebra generated by random variables

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