ELA, Volume 10, pp. 1-15, January 2003, abstract.

Conditioning Properties of the Stationary 
Distribution for a Markov Chain

Steve Kirkland

Let T be an irreducible stochastic matrix with 
stationary vector pi^T. The conditioning of pi^T 
under perturbation of T is discussed by providing 
an attainable upper bound on the absolute value of 
the derivative of each entry in pi^T with respect 
to a given perturbation matrix. Connections are 
made with an existing condition number for pi^T, 
and the results are applied to the class of Markov 
chains arising from a random walk on a tree.