MARKOV STUDY P,L
where P is a matrix file of transition probabilities determines the
class structure of the Markov chain and gives the results from the
edit line L onwards as shown in the following example:
MATRIX P
/// T1 T2 T3 T4 T5
T1 0.4 0 0 0 0.6
T2 0.9 0 0 0.1 0
T3 0 0 0.2 0.8 0
T4 0 0 0.8 0.2 0
T5 0.7 0 0 0 0.3
MAT SAVE P
MARKOV STUDY P,CUR+1
Structure of Markov chain P of 5 states:
Class structure saved in matrix file MCLASS.M
2 recurrent classes of states:
1 (2): T1 T5
2 (2): T3 T4
1 transient state:
T2
By default the results are obtained by finding the transitive closure
of the digraph determined by P.
By using the specification SVD=1 the same task is accomplished by
computing the singular value decomposition of I-P. Then also the
steady-state probabilities for each recurrent classes are calculated
and given as the second column of matrix MCLASS.M
In the above example this gives
LOADM MCLASS.M,(C7),CUR+1
Class_structure_of_P_(Transient_states=0)
Class Prob
T1 1 0.53846
T2 0 0.00000
T3 2 0.50000
T4 2 0.50000
T5 1 0.46154
M = More information on Markov chains