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Expectation is zero; left-limit of minimum (proof of Doob-Meyer decomposition, Karatzas and Shreve)

score 62 · Answer 1 · 2017-05-20 18:54:28

62

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Expectation is zero; left-limit of minimum (proof of Doob-Meyer decomposition, Karatzas and Shreve)

Published on 20 May 2017 - 18:54

score 512 · Answer 2 · 2017-05-21 08:44:13

512

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David Williams "Probability with Martingales": Martingales in $L^2$ - orthogonality of increments

Published on 21 May 2017 - 8:44

score 1.3k · Answer 3 · 2017-05-21 17:51:26

1.3k

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Question related to Polya urn model

Published on 21 May 2017 - 17:51

score 190 · Answer 4 · 2026-02-23 17:03:15

190

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Show that $\sup\limits_t\left|X_t^n\right|\to0$ in probability iff $\lim\limits_{t\to\infty}[X^n]_t\to0$ in probability when $n\to\infty$

Published on 23 Feb 2026 - 17:03

score 1.4k · Answer 5 · 2026-02-23 16:59:42

1.4k

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If $M$ is an $L^2$-bounded continuous local martingale, then $M^2-[M]$ is uniformly integrable

Published on 23 Feb 2026 - 16:59

score 274 · Answer 6 · 2017-05-23 20:20:24

274

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A bounded continuous square integrable martingale has uniformly bounded quadratic variation on bounded intervals

Published on 23 May 2017 - 20:20

score 237 · Answer 7 · 2017-05-24 00:34:30

237

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Setwise convergence with martingales

Published on 24 May 2017 - 0:34

score 43 · Answer 8 · 2017-05-26 12:02:36

43

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Useful methods to show convergence using martingales

Published on 26 May 2017 - 12:02

score 193 · Answer 9 · 2017-05-26 22:16:00

193

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$E(X_t^2)=tE(X_1^2)$ for a martingale $X$ with stationary and independent increments

Published on 26 May 2017 - 22:16

score 446 · Answer 10 · 2017-05-27 23:37:20

446

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Almost sure convergence in the martingale convergence theorem

Published on 27 May 2017 - 23:37

score 242 · Answer 11 · 2017-05-28 12:57:35

242

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Generalizing Doob's super-martingale inequality

Published on 28 May 2017 - 12:57

score 1.4k · Answer 12 · 2026-03-31 05:48:56

1.4k

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Show that the following process is a martingale without Ito's formula

Published on 31 Mar 2026 - 5:48

score 134 · Answer 13 · 2017-05-31 21:10:23

134

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Compute $E\tau e^{-\lambda \tau}$, where $\tau = \inf\{t >0 : |W_t| = 1\}$

Published on 31 May 2017 - 21:10

score 448 · Answer 14 · 2017-06-01 22:29:30

448

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Problem - Expected value and Martingales

Published on 01 Jun 2017 - 22:29

score 512 · Answer 15 · 2026-02-23 15:03:20

512

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Is a local continuous martingale square integrable.

Published on 23 Feb 2026 - 15:03

List Question

Expectation is zero; left-limit of minimum (proof of Doob-Meyer decomposition, Karatzas and Shreve)

David Williams "Probability with Martingales": Martingales in $L^2$ - orthogonality of increments

Question related to Polya urn model

Show that $\sup\limits_t\left|X_t^n\right|\to0$ in probability iff $\lim\limits_{t\to\infty}[X^n]_t\to0$ in probability when $n\to\infty$

If $M$ is an $L^2$-bounded continuous local martingale, then $M^2-[M]$ is uniformly integrable

A bounded continuous square integrable martingale has uniformly bounded quadratic variation on bounded intervals

Setwise convergence with martingales

Useful methods to show convergence using martingales

$E(X_t^2)=tE(X_1^2)$ for a martingale $X$ with stationary and independent increments

Almost sure convergence in the martingale convergence theorem

Generalizing Doob's super-martingale inequality

Show that the following process is a martingale without Ito's formula

Compute $E\tau e^{-\lambda \tau}$, where $\tau = \inf\{t >0 : |W_t| = 1\}$

Problem - Expected value and Martingales

Is a local continuous martingale square integrable.

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