T11 - Tutorial 11. 11/24/2008 Application of Eigenvalues...

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Tutorial 11. 11/24/2008 Application of Eigenvalues and Eigenvectors – part I
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Markov Chain { Definition: z A Markov Process (Markov Chain) is a process having the Markov property, which means that, given the present state , future states are independent of the past states . z Assume there are states. Define the probability of going from state i to state j in k time steps as z And the single-step transition as
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Markov Chain - Cont’d { Define and , then, it satisfies the Chapman-Kolmogorov equation: { If the state vector in period k is z is the probability that the system is in state i in period k. { Thus, , the transition matrix and the initial state completely determine every other state
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{ Does a Markov process reach equilibrium ? z The existence of steady-state probability vector, such that . { Regular Markov Chain z An square matrix is called regular if for some m, all entries of are positive. z
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This note was uploaded on 11/13/2010 for the course SEEM SEEM2018 taught by Professor Chan during the Spring '10 term at CUHK.

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T11 - Tutorial 11. 11/24/2008 Application of Eigenvalues...

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