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newstationary

# newstationary - C\work\stationary.m Page 1 3:45:49 PM...

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C:\work\stationary.m Page 1 July 11, 2003 3:45:49 PM function v = stationary(P) % % This is a MATLAB function that calculates the stationary probability vect or 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 finite-state Markov chain, the condition is that the chain be irred ucible. % % To solve the system of n equations in n unknowns, we use the matrix inver se function inv. % For a square matrix A, inv(A)*A = I, where I is the identity matrix (1's on the diagonal, 0's elsewhere). % % 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. PP = P; PP(:,end) = []; w = ones(n,1); PP = [PP w]; % PP is the matrix P with the last column replaced by a column of 1's. % % Note that for the desired v, v*PP equals v except the last element is 1.

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