function v = stationary(P)
%
% This is a MATLAB function that calculates the stationary probability vector v
% of a Markov chain transition matrix P, i.e., we solve v = v*P .
% We assume the existence of a unique stationary vector.
% For a finitestate Markov chain, the condition is that the chain be irreducible.
%
% There is a shorter program in stat.m
% This program uses the inverse of a square matrix.
% For a square matrix A, inv(A)*A = I, where I is the identity matrix (1's on the diagonal, 0's elsewhere).
% The other program stat.m uses the solve functions b/A and A\b
%
%
% We input the matrix P when we call the function.
% First find the number n of rows in the transition matrix P.
s = size(P);
n = s(1);
%
% There is one redundant equation in the n equations v = vP.
% We fill gap by using the fact that v(1) + .
.. + v(n) = 1.
% We eliminate redundant equation by replacing last column of P with ones.
% That keeps the matrix square.
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This note was uploaded on 01/16/2012 for the course IEOR 4106 taught by Professor Whitward during the Spring '11 term at Columbia College.
 Spring '11
 WhitWard

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