Discussion Notes 7

# Discussion Notes 7 - EE132B Recitation 7 Discrete Time...

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EE132B - Recitation 7 Discrete Time Markov Chains Prof. Izhak Rubin [email protected] Electrical Engineering Department UCLA

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Markov Chains { } A stochastic process (SP) is a collection of random variables over some index set. , 0,1,2,. .. is a discrete time stochastic process if states assumes values from a countable state space 0,1, k X X k S = = = g g { } 2,. .. ( 29 ( 29 1 0 1 2 1 is considered to be a Markov Chain if it satisfies the : Future evolution of the process is independent of the past given the p Mar resent : | , ko , ,. v Prope .., | : rty n n n n X DTMC P X j X X X X P X j X CTMC P + + = = = g g g ( 29 ( 29 | , | t s u t s t X j X u t P X j X + + = = = k X k X 1 X 2 X 3 X 4 X 5 1 2 3 1 2 3 4 5
( 29 ( 29 ( 29 ( 29 1 1 0 The one-step transition probability is independent of . , , Given a time homogeneous state space = {1, 2, 3}, the transition probability function (TPF) and state diagram n n n n P i j P X j X i P X j X i P i j + = = = = = = = g

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## This note was uploaded on 11/11/2010 for the course EE 132B taught by Professor Izhakrubin during the Spring '09 term at UCLA.

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Discussion Notes 7 - EE132B Recitation 7 Discrete Time...

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