*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
**

**Sammanfattning:**

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 S_{1} 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 m_{S1} (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 S_{1}
is a single state, the resulting bound is of the same order as a certain eigenvalue ratio.