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Problem 2. Let B = (N, F, (Ft), (B₂), P) be a Brownian motion. 1. Fix any T>0, and compute E (IBT>0 Ft), 0≤t≤T. 2. If is the distribution function of the standard normal N(0, 1), let Mt := Þ √P-1). Prove that (Mt, Ft)o

Problem 2. Let B = (N, F, (Ft), (B₂), P) be a Brownian motion. 1. Fix any T>0, and compute E (IBT>0 Ft), 0≤t≤T. 2. If is the distribution function of the standard normal N(0, 1), let Mt := Þ √P-1). Prove that (Mt, Ft)o

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
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Problem 2. Let B = (N, F, (Ft), (Bt), P) be a Brownian motion. 1. Fix any T>0, and compute E (IBT>0 Ft), 0≤t≤T. 2. If is the distribution function of the standard normal N(0, 1), let - + (P-₁). √T T-t Prove that (Mt, Ft)0<t<T is a uniformly integrable martingale. Find lim Mt, P- a.s. t-T- Mt := 0 ≤ t ≤T.
Transcribed Image Text:Problem 2. Let B = (N, F, (Ft), (Bt), P) be a Brownian motion. 1. Fix any T>0, and compute E (IBT>0 Ft), 0≤t≤T. 2. If is the distribution function of the standard normal N(0, 1), let - + (P-₁). √T T-t Prove that (Mt, Ft)0<t<T is a uniformly integrable martingale. Find lim Mt, P- a.s. t-T- Mt := 0 ≤ t ≤T.
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