List questions from martingales

Published on 08 Apr 2026 - 4:55

51

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Limit of conditional expectation of uniform random variable

Published on 13 Apr 2026 - 19:31

110

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distribution function of $X_t = B_t^2 - t$

Published on 17 Jan 2022 - 23:55

63

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Almost-sure convergence of a series of log-normal random variables

Published on 27 Mar 2026 - 7:49

72

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Why is this random variable integrable in a martingale?

Published on 18 Jan 2022 - 4:11

155

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Martingale representation theorem with respect to different Brownian motion, than the one generating filtration?

Published on 12 Apr 2026 - 22:52

317

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Stochastic integral change of variable.

Published on 10 Apr 2026 - 13:46

135

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$\lim_{n \to \infty}E[f(X_1,X_2)|\mathcal{F}_n]=E[f(X_1,X_2)]$ a.s.

Published on 20 Jan 2022 - 4:40

288

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Showing that a series of random variables converges almost surely.

Published on 13 Apr 2026 - 9:13

80

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Betting system and upper bounds

Published on 13 Apr 2026 - 3:13

104

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Application of martingale theory

Published on 11 Apr 2026 - 5:25

58

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What does $\phi_{W}(\mu t) = G(\phi_{W}(t))$ tell us/why is it useful? (Grimmett and Stirzaker 7.8.5)

Published on 13 Apr 2026 - 12:16

97

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How to rigorously argue that supremum of a integrable nonnegative supermartingale $M^n$ is finite

Published on 22 Jan 2022 - 22:52

133

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Orthogonal basis for $L^2$-martingales (martingale-Hardy space)

Published on 26 Mar 2026 - 4:32

147

Views

Why is the factor in Doob‘s classical $L^p$ inequality optimal?

Published on 13 Apr 2026 - 17:48

List Question

Understanding proof of discrete optimal sampling theorem

Limit of conditional expectation of uniform random variable

distribution function of $X_t = B_t^2 - t$

Almost-sure convergence of a series of log-normal random variables

Why is this random variable integrable in a martingale?

Martingale representation theorem with respect to different Brownian motion, than the one generating filtration?

Stochastic integral change of variable.

$\lim_{n \to \infty}E[f(X_1,X_2)|\mathcal{F}_n]=E[f(X_1,X_2)]$ a.s.

Showing that a series of random variables converges almost surely.

Betting system and upper bounds

Application of martingale theory

What does $\phi_{W}(\mu t) = G(\phi_{W}(t))$ tell us/why is it useful? (Grimmett and Stirzaker 7.8.5)

How to rigorously argue that supremum of a integrable nonnegative supermartingale $M^n$ is finite

Orthogonal basis for $L^2$-martingales (martingale-Hardy space)

Why is the factor in Doob‘s classical $L^p$ inequality optimal?

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