Question

Let $\exp( i u X_{t}+\frac{1}{2}u^{2}t)$ be a local martingale for any $u$, show that $X_{t}$ is a Brownian motion

score 115 · Answer 1 · 2026-04-15 23:46:06

115

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Let $\exp( i u X_{t}+\frac{1}{2}u^{2}t)$ be a local martingale for any $u$, show that $X_{t}$ is a Brownian motion

Published on 15 Apr 2026 - 23:46

score 110 · Answer 2 · 2026-04-09 15:27:55

110

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Solving a stochastic differential equation using Ito’s formula

Published on 09 Apr 2026 - 15:27

score 165 · Answer 3 · 2026-04-14 19:09:02

165

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Exponential martingale is closed iff $\mathbb{E}M_{\sigma_a}=1$

Published on 14 Apr 2026 - 19:09

score 123 · Answer 4 · 2026-04-13 05:26:08

123

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Compute integral with correlated brownian motions

Published on 13 Apr 2026 - 5:26

score 77 · Answer 5 · 2026-04-12 09:19:39

77

Views

Functional of BM and time is martingale

Published on 12 Apr 2026 - 9:19

score 191 · Answer 6 · 2026-04-14 20:42:56

191

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What is $P[B(t)>y, \land_{0 \leq u \leq t} B(u)>0|B(0)=x]$, where $B(t)$ i standard Brownian motion?

Published on 14 Apr 2026 - 20:42

score 35 · Answer 7 · 2026-04-10 21:51:30

35

Views

Large Deviation Principle for the Empirical Path Law. Brownian Particles.

Published on 10 Apr 2026 - 21:51

score 837 · Answer 8 · 2026-04-11 01:48:36

837

Views

Understanding this proof of the reflection principle

Published on 11 Apr 2026 - 1:48

score 30 · Answer 9 · 2026-04-16 08:03:04

30

Views

$\{X_t\}$ Brownian motion implies that $X_{t_1},X_{t_2},\dotsc, X_{t_n}$ are independent when $t_k<t_{k+1}$?

Published on 16 Apr 2026 - 8:03

score 90 · Answer 10 · 2026-04-15 20:18:29

90

Views

In the construction of Brownian Motion: Show that the increment vector is a Gaussian vector

Published on 15 Apr 2026 - 20:18

score 90 · Answer 11 · 2026-04-16 17:23:09

90

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Set $M_t = 4B_t^2 + e^{4B_t -8t} -4t$. Find $\mathbb{E}(M_\sigma)$ for $\sigma = \inf(t \geq 0 : |B_t| = 1)$.

Published on 16 Apr 2026 - 17:23

score 209 · Answer 12 · 2026-04-16 00:53:41

209

Views

Let $B = (B_t)_{t \geq 0}$ be a standard brownian motion and $I_t = \inf_{0 \leq s \leq t} B_s$, show $F(t, B_t, I_t)$ is a martingale.

Published on 16 Apr 2026 - 0:53

score 1.3k · Answer 13 · 2026-04-17 15:02:39

1.3k

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What is the expectation of $B_s^2B_t^2$ where $B_t$ is a standard Brownian motion?

Published on 17 Apr 2026 - 15:02

score 145 · Answer 14 · 2026-04-17 01:10:59

145

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Calculating $E(1+M_t)^2\int_0^t M_s^2 ds$ and $E(1+M_t)^2\int_0^t M_s^2 dM_s$

Published on 17 Apr 2026 - 1:10

score 493 · Answer 15 · 2026-04-09 01:57:29

493

Views

moments of a Geometric brownian motion using Ito's lemma

Published on 09 Apr 2026 - 1:57

List Question

Let $\exp( i u X_{t}+\frac{1}{2}u^{2}t)$ be a local martingale for any $u$, show that $X_{t}$ is a Brownian motion

Solving a stochastic differential equation using Ito’s formula

Exponential martingale is closed iff $\mathbb{E}M_{\sigma_a}=1$

Compute integral with correlated brownian motions

Functional of BM and time is martingale

What is $P[B(t)>y, \land_{0 \leq u \leq t} B(u)>0|B(0)=x]$, where $B(t)$ i standard Brownian motion?

Large Deviation Principle for the Empirical Path Law. Brownian Particles.

Understanding this proof of the reflection principle

$\{X_t\}$ Brownian motion implies that $X_{t_1},X_{t_2},\dotsc, X_{t_n}$ are independent when $t_k<t_{k+1}$?

In the construction of Brownian Motion: Show that the increment vector is a Gaussian vector

Set $M_t = 4B_t^2 + e^{4B_t -8t} -4t$. Find $\mathbb{E}(M_\sigma)$ for $\sigma = \inf(t \geq 0 : |B_t| = 1)$.

Let $B = (B_t)_{t \geq 0}$ be a standard brownian motion and $I_t = \inf_{0 \leq s \leq t} B_s$, show $F(t, B_t, I_t)$ is a martingale.

What is the expectation of $B_s^2B_t^2$ where $B_t$ is a standard Brownian motion?

Calculating $E(1+M_t)^2\int_0^t M_s^2 ds$ and $E(1+M_t)^2\int_0^t M_s^2 dM_s$

moments of a Geometric brownian motion using Ito's lemma

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