# 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. ### KevinGuest

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
obtain
the invariant distribution Pi. The transition probability is just a
multinormial
distribution. I am just thinking to transform it to a continuous state
space
so that to get a continuous function of Pi. We already prove that the
discrete
state space MC has an invariant distribution. Does it also have a Pi
function
for the continous state space counterpart? Or under what conditions can
we find this Pi function?