Question

Joint Density function of Brownian motion with drift and it's running maximum

score 623 · Answer 1 · 2026-03-28 12:02:57

623

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Joint Density function of Brownian motion with drift and it's running maximum

Published on 28 Mar 2026 - 12:02

score 153 · Answer 2 · 2026-03-26 01:28:19

153

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Question about Doob's decomposition and a theorem in Durrett

Published on 26 Mar 2026 - 1:28

score 112 · Answer 3 · 2019-08-26 11:52:02

112

Views

Proving $E((X_\tau-X_0)^2)=E(\langle X\rangle_\tau)$ fails if $E(\langle X\rangle_{\tau})=\infty$

Published on 26 Aug 2019 - 11:52

score 100 · Answer 4 · 2019-08-29 00:14:56

100

Views

How to show the following is a martingale

Published on 29 Aug 2019 - 0:14

score 159 · Answer 5 · 2019-08-29 07:37:56

159

Views

A question about application of Levy's $0-1$ law

Published on 29 Aug 2019 - 7:37

score 255 · Answer 6 · 2019-08-30 00:25:06

255

Views

What is a martingale measure? And in particular what is a $L^2(P)$ valued sigma-finite measure?

Published on 30 Aug 2019 - 0:25

score 362 · Answer 7 · 2019-09-01 00:08:03

362

Views

Question about asymmetric random walk and gambler's ruin

Published on 01 Sep 2019 - 0:08

score 35 · Answer 8 · 2019-09-07 22:09:42

35

Views

What is the idea behind $\mathbb E[X\mid \mathcal{A}]$ being $\mathcal{A}$-measurable

Published on 07 Sep 2019 - 22:09

score 137 · Answer 9 · 2019-09-08 11:02:57

137

Views

A reverse Azuma's inequality for martingale

Published on 08 Sep 2019 - 11:02

score 135 · Answer 10 · 2026-03-25 23:42:13

135

Views

Show that the stopping moment $\tau$ is finite, find the distribution of $X_{\tau}$, calculate $\mathbb{E}e^{\tau}$.

Published on 25 Mar 2026 - 23:42

score 511 · Answer 11 · 2026-03-26 19:15:46

511

Views

Comparison between Stochastic Calculus books

Published on 26 Mar 2026 - 19:15

score 781 · Answer 12 · 2026-03-28 15:21:12

781

Views

If $(B_t)$ is a Brownian motion and adapted to the filtration $(\mathcal F_t)$ does $B_t-B_s$ is independent of $\mathcal F_s$?

Published on 28 Mar 2026 - 15:21

score 63 · Answer 13 · 2026-03-28 21:06:57

63

Views

Prove that $(B_t)$ is a brownian motion $\iff$ $(B_t)$ and $(B_t^2-t)$ are continuous martingale.

Published on 28 Mar 2026 - 21:06

score 300 · Answer 14 · 2019-09-11 22:02:38

300

Views

Martingale Convergence Theorem proof doubt

Published on 11 Sep 2019 - 22:02

score 635 · Answer 15 · 2019-09-14 15:07:18

635

Views

One type of Optional Sampling Theorem

Published on 14 Sep 2019 - 15:07

List Question

Joint Density function of Brownian motion with drift and it's running maximum

Question about Doob's decomposition and a theorem in Durrett

Proving $E((X_\tau-X_0)^2)=E(\langle X\rangle_\tau)$ fails if $E(\langle X\rangle_{\tau})=\infty$

How to show the following is a martingale

A question about application of Levy's $0-1$ law

What is a martingale measure? And in particular what is a $L^2(P)$ valued sigma-finite measure?

Question about asymmetric random walk and gambler's ruin

What is the idea behind $\mathbb E[X\mid \mathcal{A}]$ being $\mathcal{A}$-measurable

A reverse Azuma's inequality for martingale

Show that the stopping moment $\tau$ is finite, find the distribution of $X_{\tau}$, calculate $\mathbb{E}e^{\tau}$.

Comparison between Stochastic Calculus books

If $(B_t)$ is a Brownian motion and adapted to the filtration $(\mathcal F_t)$ does $B_t-B_s$ is independent of $\mathcal F_s$?

Prove that $(B_t)$ is a brownian motion $\iff$ $(B_t)$ and $(B_t^2-t)$ are continuous martingale.

Martingale Convergence Theorem proof doubt

One type of Optional Sampling Theorem

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