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1 IEOR 6711: Continuous-Time Markov Chains

Copyrightc 2009 by Karl Sigman1 IEOR 6711 : Continuous-Time Markov ChainsA Markov chain in discrete time ,{Xn:n 0}, remains in any state for exactly oneunit of time before making a transition (change of state). We proceed now to relax thisrestriction by allowing a chain to spend a continuous amount of time in any state, butin such a way as to retain the Markov property. As motivation, suppose we consider therat in the open maze. Clearly it is more realistic to be able to keep track of where therat is at any continuous -timet 0 as oppposed to only where the rat is aftern steps.

1 IEOR 6711: Continuous-Time Markov Chains A Markov chain in discrete time, fX n: n 0g, remains in any state for exactly one unit of time before making a transition (change of state). We proceed now to relax this restriction by allowing a chain to spend a continuous amount of time in any state, but in such a way as to retain the Markov property.

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  Time, Chain, Eori, Continuous, 6711, Markov, Ieor 6711, Continuous time markov chains

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