How to transform a discrete state space to a continuous state space Markov chain?

Discussion in 'Scientific Statistics Math' started by Kevin, Dec 17, 2003.

  1. Kevin

    Kevin Guest

    hi, everyone

    In one word, what we need is to transform a discrete state space MC to a
    continuous state space MC. Why? Because when the state space grows,
    the transition matrix will become terribly large. So it is very hard to
    the invariant distribution Pi. The transition probability is just a
    distribution. I am just thinking to transform it to a continuous state
    so that to get a continuous function of Pi. We already prove that the
    state space MC has an invariant distribution. Does it also have a Pi
    for the continous state space counterpart? Or under what conditions can
    we find this Pi function?

    Thanks for your help,

    Kevin, Dec 17, 2003
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