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.