List questions from martingales

Published on 12 Apr 2026 - 6:12

326

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Is Brownian motion a semimartingale?

Published on 09 Apr 2026 - 12:57

184

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How to find $E(\tau)$?

Published on 09 Apr 2026 - 20:10

144

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Surprisingly simple expected time for the "range" of a Brownian motion to extend beyond $a$ - is there a martingale method?

Published on 10 Apr 2026 - 17:10

207

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Relation between supremum of quadratic variation expectation with expectation of supremum of martingale

Published on 12 Apr 2026 - 22:45

255

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Stopping time and super-martingale

Published on 11 Apr 2026 - 22:02

259

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Durrett's Theorem 4.8.7 (Symmetric Simple Random Walk)

Published on 14 Apr 2026 - 0:11

117

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Filtration of sum of independent sub-martingales

Published on 12 Apr 2026 - 8:02

76

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Discrete time positive martingale with non-trivial limit

Published on 26 Mar 2026 - 9:40

78

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Supremum of Brownian motion increments

Published on 13 Apr 2026 - 8:58

31

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Proving $E\bigg[\bigg(\int_a^b X_s dW_s \bigg)^2 \ \bigg\vert \ \mathcal{F}_a \bigg] =\int_a^b (X_s)^2 ds $

Published on 07 Apr 2026 - 23:02

176

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Understanding proof of Azuma's inequality

Published on 09 Apr 2026 - 19:58

49

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Does this setup imply that $E[(M_t-M_s)^4 \mid \mathcal{F}_s]$ is bounded?

Published on 14 Apr 2026 - 6:28

24

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Proving an upper bound to the running maximum of a martingale with mean zero and finite second moment

Published on 03 Apr 2026 - 17:06

49

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For stochastic integral $I$ of simple process $X$, $0 \le s < t< \infty$, show $E[I_t(X) | \mathscr{F}_s] = I_s(X)$ a.s.

Published on 07 Apr 2026 - 22:59

List Question

Showing that a function of two brownian motions is a martingale.

Is Brownian motion a semimartingale?

How to find $E(\tau)$?

Surprisingly simple expected time for the "range" of a Brownian motion to extend beyond $a$ - is there a martingale method?

Relation between supremum of quadratic variation expectation with expectation of supremum of martingale

Stopping time and super-martingale

Durrett's Theorem 4.8.7 (Symmetric Simple Random Walk)

Filtration of sum of independent sub-martingales

Discrete time positive martingale with non-trivial limit

Supremum of Brownian motion increments

Proving $E\bigg[\bigg(\int_a^b X_s dW_s \bigg)^2 \ \bigg\vert \ \mathcal{F}_a \bigg] =\int_a^b (X_s)^2 ds $

Understanding proof of Azuma's inequality

Does this setup imply that $E[(M_t-M_s)^4 \mid \mathcal{F}_s]$ is bounded?

Proving an upper bound to the running maximum of a martingale with mean zero and finite second moment

For stochastic integral $I$ of simple process $X$, $0 \le s < t< \infty$, show $E[I_t(X) | \mathscr{F}_s] = I_s(X)$ a.s.

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