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7. Let Wt be a standard Brownian Motion. Define X, is by Xt = W², t≥ 0. a) Is Xt a Brownian Motion? b) Compute the probability density function fxt(x) of X₁.

7. Let Wt be a standard Brownian Motion. Define X, is by Xt = W², t≥ 0. a) Is Xt a Brownian Motion? b) Compute the probability density function fxt(x) of X₁.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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7. Let Wt be a standard Brownian Motion. Define X, is by X₁ = W², t≥ 0. a) Is Xt a Brownian Motion? b) Compute the probability density function fx, (x) of X₁. c) Compute E[(X₁), E (Xt+s — Xt), and E[(Xt+s — Xt)²] (here t ≥ 0, s ≥ 0). d) Compute E [X₁ (Xt+s – Xt)²]. Does the process X₁ have independent increments?
Transcribed Image Text:7. Let Wt be a standard Brownian Motion. Define X, is by X₁ = W², t≥ 0. a) Is Xt a Brownian Motion? b) Compute the probability density function fx, (x) of X₁. c) Compute E[(X₁), E (Xt+s — Xt), and E[(Xt+s — Xt)²] (here t ≥ 0, s ≥ 0). d) Compute E [X₁ (Xt+s – Xt)²]. Does the process X₁ have independent increments?
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