m**a
发帖数: 1840 | 1 Consider a discrete-time Markov process with continuous state space (say, [0
,1]). The transition has the property that given the current state, the
possible realization of the next state is finite.
Through some numerical simulations, I found that for certain discrete-time
Markov process with the above transition property, the stationary
distribution is concentrated on a finite number of states. Is there a theory
that I can use to determine whether such a concentration phenomenon happens
or not | d****y
发帖数: 53 | 2 I would simply solve
p_i = \sum_j p_j M_{ji}
(where the indices i,j can be both continuous and discrete)
for the stationary distribution. It suffices to make the ansatz that the
distribution has atom mass at a few states and zero elsewhere and proceed to
solve for such a solution
[0
theory
happens
【在 m**a 的大作中提到】
: Consider a discrete-time Markov process with continuous state space (say, [0
: ,1]). The transition has the property that given the current state, the
: possible realization of the next state is finite.
: Through some numerical simulations, I found that for certain discrete-time
: Markov process with the above transition property, the stationary
: distribution is concentrated on a finite number of states. Is there a theory
: that I can use to determine whether such a concentration phenomenon happens
: or not
| m**a
发帖数: 1840 | 3 But the problem is that I don't know the number of those states and their
location.
to
【在 d****y 的大作中提到】
: I would simply solve
: p_i = \sum_j p_j M_{ji}
: (where the indices i,j can be both continuous and discrete)
: for the stationary distribution. It suffices to make the ansatz that the
: distribution has atom mass at a few states and zero elsewhere and proceed to
: solve for such a solution
:
: [0
: theory
: happens
|
|
