List questions from brownian-motion

Published on 07 Jul 2015 - 12:10

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Itô integral with respect to a diffusion

Published on 07 Jul 2015 - 21:04

42

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Notation in stochastic integrals

Published on 02 Apr 2026 - 17:40

455

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Why is the solution of a stochastic differential equation wrt the Brownian motion suitable for a model of a disturbed time continuous process

Published on 02 Apr 2026 - 17:46

317

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Quadratic variation of the Brownian motion and Itō's lemma

Published on 02 Apr 2026 - 17:46

385

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harmonic functions and ito formula

Published on 07 Apr 2026 - 22:21

70

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The Itō integral $\sum_{i=1}^nH_{t_{i-1}}\left(B_{t_i}-B_{t_{i-1}}\right)$ of an simple process $H$ is independent of the choice of $(t_0,\ldots,t_n)$

Published on 02 Apr 2026 - 17:44

1.2k

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Moment Generating Function for Brownian motion's exit of interval.

Published on 29 Mar 2026 - 7:33

386

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Expectation of a product involving Brownian motion

Published on 10 Jul 2015 - 23:27

70

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Integration of Brownian Motion with a function of t

Published on 11 Jul 2015 - 20:38

232

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Proof of Itō's lemma for the Brownian motion

Published on 02 Apr 2026 - 17:48

7.6k

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Show that $X(t)=t W(1/t)$ is a Brownian motion if $W(t)$ is a Brownian motion.

Published on 12 Jul 2015 - 16:26

78

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Show that $\lim_{|P|\to 0}\sum_{k=0}^{n-1}\frac{W(t_{k+1})+W(t_k)}{2}\left[W(t_{k+1})-W(t_k)\right]=\frac{W^2(T)}{2}$

Published on 13 Jul 2015 - 9:29

484

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Why does dZ(t)dt=(dt)^2=0

Published on 23 Feb 2026 - 12:02

567

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Mean Squared Displacement of Biased Random Walk

Published on 03 Apr 2026 - 2:13

List Question

Itô symmetry for elementary predictable stochastic processes

Itô integral with respect to a diffusion

Notation in stochastic integrals

Why is the solution of a stochastic differential equation wrt the Brownian motion suitable for a model of a disturbed time continuous process

Quadratic variation of the Brownian motion and Itō's lemma

harmonic functions and ito formula

The Itō integral $\sum_{i=1}^nH_{t_{i-1}}\left(B_{t_i}-B_{t_{i-1}}\right)$ of an simple process $H$ is independent of the choice of $(t_0,\ldots,t_n)$

Moment Generating Function for Brownian motion's exit of interval.

Expectation of a product involving Brownian motion

Integration of Brownian Motion with a function of t

Proof of Itō's lemma for the Brownian motion

Show that $X(t)=t W(1/t)$ is a Brownian motion if $W(t)$ is a Brownian motion.

Show that $\lim_{|P|\to 0}\sum_{k=0}^{n-1}\frac{W(t_{k+1})+W(t_k)}{2}\left[W(t_{k+1})-W(t_k)\right]=\frac{W^2(T)}{2}$

Why does dZ(t)dt=(dt)^2=0

Mean Squared Displacement of Biased Random Walk

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