function
absorbing(Q, R)
%
% This is a MATLAB function that calculates important characteristics
% of an absorbing Markov chain.
%
% The full Markov chain transition matrix P is assumed to be (k+m) by (k+m).
% The first k states are absorbing states; the last m states are
% transient states.
% The matrix P is divided into 4 submatrices: k by k, k by m, m by k and m by m.
% The upper left submatrix is a k by k identity matrix (1's on the diagonal;
% 0's elsewhere).
% The upper right submatrix is a k by m matrix of all 0's.
% The lower left submatrix is an m by k matrix R.
% The lower right submatrix is an m by m matrix Q.
% We input the matrices Q and R as data to the function.
% The matrix Q gives the transition probabilities among the m transient states.
% The matrix R gives the onestep transition probabilities from the m
% transient states to the k absorbing states.
%
% Given the absorbing Markov chain characterized by the two matrices Q and R,
% we calculate three matrices describing the behavior of the Markov chain.
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 Spring '11
 WhitWard

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