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Consider a discrete time, ergodic Markov chain with finite state space whichis started from stationarity. Fill and Lyzinski (2014) showed that, in somecases, the hitting time for a given state may be represented as a sum of ageometric number of IID random variables. We extend this result by givingexplicit bounds on the distance between any such hitting time and anappropriately chosen geometric sum, along with other related approximations.The compounding random variable in our approximating geometric sum is a strongstationary time for the underlying Markov chain; we also discuss theapproximation and construction of this distribution.

On strong stationary times and approximation of Markov chain hitting times by geometric sums