Question

Brownian motion and conditional probability

score 2.3k · Answer 1 · 2026-04-12 07:02:22

2.3k

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Brownian motion and conditional probability

Published on 12 Apr 2026 - 7:02

score 80 · Answer 2 · 2026-04-16 00:14:57

80

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Showing that $\text{Var}(X_t) = t$ if $(X_t)_{t > 0}$ is a gaussian process

Published on 16 Apr 2026 - 0:14

score 3.6k · Answer 3 · 2026-04-15 15:47:59

3.6k

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Calculating Expectation and Variance of $S_t$, stochastic differential equation.

Published on 15 Apr 2026 - 15:47

score 416 · Answer 4 · 2026-04-17 15:33:43

416

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How to show that $P(B_1>0, B_2<0)= P(B_1>0)P(B_2-B_1 <0) P(|B_2 - B_1| > |B_1|)$?

Published on 17 Apr 2026 - 15:33

score 3.7k · Answer 5 · 2026-04-15 23:41:10

3.7k

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Is $W^2-t$ martingale?

Published on 15 Apr 2026 - 23:41

score 199 · Answer 6 · 2026-04-17 10:25:49

199

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f I$M,N$ are local martingale, then so is $N+M$ but not $NM$.

Published on 17 Apr 2026 - 10:25

score 548 · Answer 7 · 2026-04-16 22:05:08

548

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To show martingale, what other conditions do you need to check if the process has zero drift?

Published on 16 Apr 2026 - 22:05

score 211 · Answer 8 · 2026-04-13 06:23:19

211

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Explain in words why $2^{W_t}$ is not a martingale

Published on 13 Apr 2026 - 6:23

score 112 · Answer 9 · 2026-03-26 23:02:07

112

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Doob's Optional Sample Theorem

Published on 26 Mar 2026 - 23:02

score 324 · Answer 10 · 2026-03-25 12:49:09

324

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How to Understand the Gambler Ruin Problem

Published on 25 Mar 2026 - 12:49

score 2.3k · Answer 11 · 2026-04-14 16:38:07

2.3k

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Question About Proving $\exp(aW(t)-\frac{a^{2t}}{2})$ is Martingale

Published on 14 Apr 2026 - 16:38

score 89 · Answer 12 · 2026-04-09 12:01:05

89

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Is it possible to define unitary operator-valued stochastic process and related stochastic differential equations?

Published on 09 Apr 2026 - 12:01

score 126 · Answer 13 · 2026-04-17 05:43:32

126

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Given a prob measure P and a P-UI martingale $\{ \rho_t \}$ define $Q \sim P$ s.t. $E[\frac{dQ}{dP}|\mathscr{F}_t]=\rho_t$

Published on 17 Apr 2026 - 5:43

score 68 · Answer 14 · 2026-04-15 22:03:08

68

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Find $\mathbb{E}[T_1|X(1)=2]$ where $X(t)$ be the Poisson process.

Published on 15 Apr 2026 - 22:03

score 52 · Answer 15 · 2026-04-16 21:14:26

52

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Show that $(X_{\sigma\wedge n },\mathcal{F}_n)_n $ is martingal and $(\|X_{\sigma\wedge n }\|,\mathcal{F}_n)_n $ is a sub-martingal.

Published on 16 Apr 2026 - 21:14

List Question

Brownian motion and conditional probability

Showing that $\text{Var}(X_t) = t$ if $(X_t)_{t > 0}$ is a gaussian process

Calculating Expectation and Variance of $S_t$, stochastic differential equation.

How to show that $P(B_1>0, B_2<0)= P(B_1>0)P(B_2-B_1 <0) P(|B_2 - B_1| > |B_1|)$?

Is $W^2-t$ martingale?

f I$M,N$ are local martingale, then so is $N+M$ but not $NM$.

To show martingale, what other conditions do you need to check if the process has zero drift?

Explain in words why $2^{W_t}$ is not a martingale

Doob's Optional Sample Theorem

How to Understand the Gambler Ruin Problem

Question About Proving $\exp(aW(t)-\frac{a^{2t}}{2})$ is Martingale

Is it possible to define unitary operator-valued stochastic process and related stochastic differential equations?

Given a prob measure P and a P-UI martingale $\{ \rho_t \}$ define $Q \sim P$ s.t. $E[\frac{dQ}{dP}|\mathscr{F}_t]=\rho_t$

Find $\mathbb{E}[T_1|X(1)=2]$ where $X(t)$ be the Poisson process.

Show that $(X_{\sigma\wedge n },\mathcal{F}_n)_n $ is martingal and $(\|X_{\sigma\wedge n }\|,\mathcal{F}_n)_n $ is a sub-martingal.

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