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eigenmarkov Scilab Group Scilab Function eigenmarkov
NAME
eigenmarkov - normalized left and right Markov eigenvectors
CALLING SEQUENCE
[M,Q]=eigenmarkov(P)
PARAMETERS
P : real N x N Markov matrix. Sum of entries in each row should
add to one.
M : real matrix with N columns.
Q : real matrix with N rows.
DESCRIPTION
Returns normalized left and right eigenvectors associated with the
eigenvalue 1 of the Markov transition matrix P. If the multiplicity of
this eigenvalue is m and P is N x N, M is a m x N matrix and Q a N x m
matrix. M(k,:) is the probability distribution vector associated with the
kth ergodic set (recurrent class). M(k,x) is zero if x is not in the k-th
recurrent class. Q(x,k) is the probability to end in the k-th recurrent
class starting from x. If P^k converges for large k (no eigenvalues on
the unit circle except 1), then the limit is Q*M (eigenprojection).
EXAMPLE
//P has two recurrent classes (with 2 and 1 states) 2 transient states
P=genmarkov([2,1],2)
[M,Q]=eigenmarkov(P);
P*Q-Q
Q*M-P^20
SEE ALSO
genmarkov, classmarkov
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