Question

Add a compensator to submartingale to create a martingale.

score 939 · Answer 1 · 2015-09-27 23:09:22

939

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Add a compensator to submartingale to create a martingale.

Published on 27 Sep 2015 - 23:09

score 1.9k · Answer 2 · 2015-09-30 00:31:54

1.9k

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Representation theorem for local martingales

Published on 30 Sep 2015 - 0:31

score 2k · Answer 3 · 2015-10-04 09:48:55

2k

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Proving the product of iid positive random variables converges to zero almost surely

Published on 04 Oct 2015 - 9:48

score 509 · Answer 4 · 2026-03-29 18:37:26

509

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Prove $\tau=\inf\{t\in[0,T]:M_t=0\}\wedge T$ a stopping time for a continuous martingale $(M_t)_{t \geq 0}$

Published on 29 Mar 2026 - 18:37

score 72 · Answer 5 · 2015-10-09 23:00:28

72

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How can I show that $\sup_{t \geq 0}(B^_t-\mu t^{r/2})=_{law} \sup_{v \geq 0}(\lambda B^_{v}-\mu \lambda^rv^{r/2})$

Published on 09 Oct 2015 - 23:00

score 31 · Answer 6 · 2015-10-10 11:39:48

31

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$ \sup_{t \geq 0}\big( |B_t|-t^{r/2}\big) \text{ and } \sup_{t \geq 0}\big( \frac{|B_t|}{1+t^{r/2}}\big)^\rho$ have the same law?

Published on 10 Oct 2015 - 11:39

score 72 · Answer 7 · 2026-03-18 23:56:12

72

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question about martingale inequality (similar to the condition of submartingale convergence)

Published on 18 Mar 2026 - 23:56

score 446 · Answer 8 · 2026-03-29 18:38:09

446

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Show submartingale property.

Published on 29 Mar 2026 - 18:38

score 193 · Answer 9 · 2026-03-09 20:09:34

193

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Application of Laplace transform to stopping times and expectations

Published on 09 Mar 2026 - 20:09

score 187 · Answer 10 · 2026-03-29 20:25:59

187

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Conditional expectation and stopping time $\mathbb{E}(X1_{T\leq m}|\mathcal{F}_{T\wedge m})=\mathbb{E}(X1_{T\leq m}|\mathcal{F}_T)$

Published on 29 Mar 2026 - 20:25

score 675 · Answer 11 · 2015-10-16 07:06:40

675

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Continuous nonnegative supermartingale vanishes after it hits zero

Published on 16 Oct 2015 - 7:06

score 740 · Answer 12 · 2026-03-18 23:54:32

740

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Proof of a stochastic process being a martingale

Published on 18 Mar 2026 - 23:54

score 293 · Answer 13 · 2015-10-17 23:41:19

293

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Why for a continous local martingale ,on an enlarged probability space, it possibly holds that $M_t=B_{\langle M \rangle _t}$

Published on 17 Oct 2015 - 23:41

score 206 · Answer 14 · 2026-04-03 06:56:14

206

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Most likely position for random walk with symmetric jumps after $t$ steps

Published on 03 Apr 2026 - 6:56

score 221 · Answer 15 · 2015-10-20 23:55:59

221

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Uniform Integrability and Supermartingal Process

Published on 20 Oct 2015 - 23:55

List Question

Add a compensator to submartingale to create a martingale.

Representation theorem for local martingales

Proving the product of iid positive random variables converges to zero almost surely

Prove $\tau=\inf\{t\in[0,T]:M_t=0\}\wedge T$ a stopping time for a continuous martingale $(M_t)_{t \geq 0}$

How can I show that $\sup_{t \geq 0}(B^_t-\mu t^{r/2})=_{law} \sup_{v \geq 0}(\lambda B^_{v}-\mu \lambda^rv^{r/2})$

$ \sup_{t \geq 0}\big( |B_t|-t^{r/2}\big) \text{ and } \sup_{t \geq 0}\big( \frac{|B_t|}{1+t^{r/2}}\big)^\rho$ have the same law?

question about martingale inequality (similar to the condition of submartingale convergence)

Show submartingale property.

Application of Laplace transform to stopping times and expectations

Conditional expectation and stopping time $\mathbb{E}(X1_{T\leq m}|\mathcal{F}_{T\wedge m})=\mathbb{E}(X1_{T\leq m}|\mathcal{F}_T)$

Continuous nonnegative supermartingale vanishes after it hits zero

Proof of a stochastic process being a martingale

Why for a continous local martingale ,on an enlarged probability space, it possibly holds that $M_t=B_{\langle M \rangle _t}$

Most likely position for random walk with symmetric jumps after $t$ steps

Uniform Integrability and Supermartingal Process

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