Tid: 22 oktober 2001 kl 1515-1700
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Torkel Erhardsson, Matematisk statistik, KTH
Titel: Strong memoryless times and rare events in stationary Markov renewal processes
In an earlier talk on November 6, 2000, I gave a bound for the total variation distance between the distribution of the accumulated reward of a stationary renewal-reward process in discrete or continuous time, and a compound Poisson distribution. The bound can be applied to the amount of time spent by a stationary finite-state Markov process in a ``rare'' subset S1 of the state space, since this amount can be expressed as an accumulated reward. In this case, the bound is easy to calculate explicitly, and is of order close to mS1 (where m is the stationary distribution), provided that the state space contains at least one frequently visited state.
In this talk, I will show how an efficient bound can be derived when the latter condition does not hold. The main idea is to embed the Markov process into a Markov renewal process on an enlarged state space, such that the condition does hold, using auxiliary random variables called strong memoryless times. If the Markov process is time-reversible, and S1 is a single state, the resulting bound is of the same order as a certain eigenvalue ratio.
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