2.15 A symmetric random walk fSnjn 5 0; 1; 2; ...g starts at the position S0 5...

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2.15 A symmetric random walk fSnjn 5 0; 1; 2; ...g starts at the position S0 5 k and ends when the walk first reaches either the origin or the position m, where 0 , k , m. Let T be defined by T 5 minfnjSn 5 0 or mg That is, T is the stopping time.

a. Show that E½ST 5 k.

b. Define Yn 5 S2 n 2 n and show that fYng is a martingale with respect to fSng.

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Markov Processes For Stochastic Modeling

ISBN: 9780323282956

2nd Edition

Authors: Oliver Ibe

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Question Posted: Nov 06, 2024 08:00 AM

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2.15 A symmetric random walk fSnjn 5 0; 1; 2; ...g starts at the position S0 5...

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Markov Processes For Stochastic Modeling

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