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Lecture 4: Continuous-time Markov Chains

Lecture 4: Continuous-time Markov Chains

cims.nyu.edu

Lecture 4: Continuous-time Markov Chains Readings Grimmett and Stirzaker (2001) 6.8, 6.9. Options: Grimmett and Stirzaker (2001) 6.10 (a survey of the issues one needs to address to make the discussion below rigorous) Norris (1997) Chapter 2,3 (rigorous, though readable; this is the classic text on Markov chains, both discrete and continuous)

  Lecture, Time, Chain, Continuous, Lecture 4, Markov, Continuous time markov chains

1 IEOR 6711: Continuous-Time Markov Chains

1 IEOR 6711: Continuous-Time Markov Chains

www.columbia.edu

independent of the past, and so on.1 Letting X(t) denote the state at time t, we end up with a continuous-time stochastic process fX(t) : t 0gwith state space S. Our objective is to place conditions on the holding times to ensure that the continuous-time process satis es the Markov property: The future, fX(s+ t) : t 0g, given the

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

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