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First Passage Probabilities

Let: T = Set of Transient States
       Tc= Set of Recurrent States

Output: The first passage probabilities to recurrent state j given X(0) = i, for all i in the set T and j in the set Tc.

Input: Q and R, where:
Q = submatrix of transion probabilities between transient states of the one-step transition probability matrix P.
R = submatrix of transition probabilities from transient states to recurrent states of the one-step transition probability matrix P.

Submatrix (Q):

Submatrix (R):

Results will appear below.

Results