summary_of_continuous_M.C.

summary_of_continuous_M.C. - Summer 2007 STAT333 Summary of...

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Summer 2007 STAT333 Summary of the continuous Markov chain We already had a summary of the discrete Markov Chain. Almost all of deFnitions and results in the discrete Markov chain can be extended to the continuous Markov chain. Let me just review some special things in continuous Markov Chain. ±or continuous Markov chain, we are interested in the following two things: 1. how long are you going to stay in state i , starting from state i ? 2. which place will the process enter into if the process is going to leave the current place? Knowing the above two things can help us to learn everything about the continuous Markov Chain. All the answers contain in the generator or the rate matrix R . Rate matrix ( R ). (a) DeFnition: R = lim h 0 + P ( h ) I h , where P ( h )isthe h -step transition matrix and I is the identity matrix. (b) Properties: i. r ii 0, for i S (state space); ii. r ij 0, for i, j S and i ± = j ; iii. j S r ij =0.
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summary_of_continuous_M.C. - Summer 2007 STAT333 Summary of...

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