Question

Brownian motions in $\mathbb{R}^2$ and Cauchy distribution

score 151 · Answer 1 · 2026-04-12 20:07:20

151

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Brownian motions in $\mathbb{R}^2$ and Cauchy distribution

Published on 12 Apr 2026 - 20:07

score 1.7k · Answer 2 · 2026-04-13 06:04:22

1.7k

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To find the Expectation of exponential of Brownian motion

Published on 13 Apr 2026 - 6:04

score 119 · Answer 3 · 2026-04-17 09:26:42

119

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Integral w.r.t. Brownian motion vanishes when taking expectation

Published on 17 Apr 2026 - 9:26

score 52 · Answer 4 · 2026-04-16 02:07:16

52

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Why $\mathbb P(X_{\tau-t}<0\mid \mathcal F_{\tau})=\frac{1}{2}$?

Published on 16 Apr 2026 - 2:07

score 60 · Answer 5 · 2026-04-13 06:00:25

60

Views

Probability of hitting time to be equal to particular $t$.

Published on 13 Apr 2026 - 6:00

score 111 · Answer 6 · 2026-04-11 06:23:27

111

Views

Exchanging limit for Brownian stochastic integral

Published on 11 Apr 2026 - 6:23

score 85 · Answer 7 · 2026-04-14 20:48:26

85

Views

Estimate price in Black-Scholes model

Published on 14 Apr 2026 - 20:48

score 1.1k · Answer 8 · 2026-04-12 13:34:50

1.1k

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For brownian motion, why $dW_{t}=\epsilon\sqrt{dt}$?

Published on 12 Apr 2026 - 13:34

score 145 · Answer 9 · 2026-04-17 22:40:04

145

Views

Is there a symmetry argument that the running minimum of a Wiener process is the negative of the running maximum of that process?

Published on 17 Apr 2026 - 22:40

score 189 · Answer 10 · 2026-04-13 05:28:03

189

Views

Let W be a standard Brownian motion. Use Itô’s formula and induction over $n\in \mathbb{N}$ to calculate $E[W^n_t]$

Published on 13 Apr 2026 - 5:28

score 21 · Answer 11 · 2026-04-14 22:35:50

21

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If $U$ is independent of $X$ does $\mathbb P(U\in A\mid X,Y)=\mathbb P(U\in A\mid X)$?

Published on 14 Apr 2026 - 22:35

score 368 · Answer 12 · 2026-04-16 03:59:20

368

Views

Let $W$ be a standard Brownian motion, compute the stochastic integral $\int_0^t s W_s^2dW_s$. Why should I use $f(t,x)=tx^3/3$?

Published on 16 Apr 2026 - 3:59

score 34 · Answer 13 · 2026-04-13 14:40:43

34

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Proof of positive probability of exit of Brownian Motion through an open subset of the boundary of a compact connected $\mathbb{R}^2$ set.

Published on 13 Apr 2026 - 14:40

score 38 · Answer 14 · 2026-04-14 23:32:31

Prove that $\mathbb P^\alpha (B_t-B_s\in U,B_s\in V)=\mathbb P^\alpha (B_t-B_s\in U)\mathbb P^\alpha (B_s\in V)$.

score 68 · Answer 15 · 2026-04-14 20:57:24

68

Views

Arbitrage-free price $V_t^X$ for classical Black-Scholes model

Published on 14 Apr 2026 - 20:57

List Question

Brownian motions in $\mathbb{R}^2$ and Cauchy distribution

To find the Expectation of exponential of Brownian motion

Integral w.r.t. Brownian motion vanishes when taking expectation

Why $\mathbb P(X_{\tau-t}<0\mid \mathcal F_{\tau})=\frac{1}{2}$?

Probability of hitting time to be equal to particular $t$.

Exchanging limit for Brownian stochastic integral

Estimate price in Black-Scholes model

For brownian motion, why $dW_{t}=\epsilon\sqrt{dt}$?

Is there a symmetry argument that the running minimum of a Wiener process is the negative of the running maximum of that process?

Let W be a standard Brownian motion. Use Itô’s formula and induction over $n\in \mathbb{N}$ to calculate $E[W^n_t]$

If $U$ is independent of $X$ does $\mathbb P(U\in A\mid X,Y)=\mathbb P(U\in A\mid X)$?

Let $W$ be a standard Brownian motion, compute the stochastic integral $\int_0^t s W_s^2dW_s$. Why should I use $f(t,x)=tx^3/3$?

Proof of positive probability of exit of Brownian Motion through an open subset of the boundary of a compact connected $\mathbb{R}^2$ set.

Prove that $\mathbb P^\alpha (B_t-B_s\in U,B_s\in V)=\mathbb P^\alpha (B_t-B_s\in U)\mathbb P^\alpha (B_s\in V)$.

Arbitrage-free price $V_t^X$ for classical Black-Scholes model

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