Calculating stationary distribution of Markov chain

I am calculating the stationary distribution of a Markov chain. The transition matrix P is sparse (at most 4 entries in every column)

The solution is the solution to the system: P*S=S

I use the following method:

St = eigs(P,1,1);
S  = St/sum(St); %S is the (normalized) stationary distribution

but i was wondering if there is a faster method... I have no clue yet how fast it is going to be, but the faster the better, because the speed will determine how accurate i can make my grid (more accurate = larger transition matrix)

thanks in advance!

Answer 1

[Oscar]

The algorithm only worked for 2 dimensions. I have written an algorithm implementing the same method and it works for all dimensions. See attached file.

Answer 2

[Oscar]

Section 6 and 7 of this document explain a method called 'state space reduction' for calculating the stationary distribution of a Markov Chain: http://www.math.wustl.edu/~feres/Math450Lect04.pdf

I have removed a typo from the program that is given in the document and now it is working. See attached file.

[Clarisha Nijman]

Dear all,

today I am working on a project and need a stable code for the stationary distribution. I tried several suggestions. This last one gives an error, but as I do not understand the details of the code, your advice is really needed. Can somebody give me some advice please?,

Thank you in advance,

PP =

    0.3333    0.1667    0.6000
    0.3333    0.5000    0.2000
    0.3333    0.3333    0.2000

>> p=limitdist(PP) In an assignment A(:) = B, the number of elements in A and B must be the same.

Error in limitdist (line 27) p(j)=sum(p(1:j1).*(P(1:j1,j)));

[yizhou yang]

Please try using this:

p(j)=sum(p(1:j1).*(P(1:j1,j))');

just need to transpose.