Let {X„}nɛN be a symmetric random walk (X, = ±1 w.p. 1/2) on (-0, 1]nZ. Set S, = D-1 Xk-a) Show that for all 0 € R%3DLk=1M = (sech 0)"e®Smis a martingale, where sech is the hyperbolic secant.b) Considerwhere T = inf{n : S, = 1}. Letting n → 0, and then 0 → 0 show that P(T < ) = 1.

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Let {X„}nɛn be a symmetric random walk (X„, a) Show that for all 0 e R ±l w.p. 1/2) on (-, 1]NZ. Set S„ =Ei=1 Xk- %3D M = (sech 0)"e®S» is a martingale, where sech is the hyperbolic secant. b) Consider where 7 = inf{n : S„ = 1}. Letting n → ∞0, and then 0 → 0 show that P(7 < ∞) = 1.

Let {X„}nɛn be a symmetric random walk (X„, a) Show that for all 0 e R ±l w.p. 1/2) on (-, 1]NZ. Set S„ =Ei=1 Xk- %3D M = (sech 0)"e®S» is a martingale, where sech is the hyperbolic secant. b) Consider where 7 = inf{n : S„ = 1}. Letting n → ∞0, and then 0 → 0 show that P(7 < ∞) = 1.

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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