Deviation Matrix of a Continuous-Time Markov Chain.

摘要

The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P(.) and ergodic matrix II is the matrix D integrated from infinity to zero (P(t)=II)dt. The authors give conditions for D to exist and discuss properties and a representation of D. The deviation matrix of a birth-death process is investigated in detail. The authors also describe a new application of deviation matrices by showing that a measure for the convergence to stationarity of a stochastically increasing Markov chain can be expressed in terms of the elements of the deviation matrix of the chain.