- Series
- Stochastics Seminar
- Time
- Thursday, January 28, 2016 - 3:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Alessandro Arlotto – Duke University
- Organizer
- Christian Houdré
We prove a central limit theorem for a class of additive processes that
arise naturally in the theory of finite horizon Markov decision problems.
The main theorem generalizes a classic result of Dobrushin (1956) for
temporally non-homogeneous Markov chains, and the principal innovation is
that here the summands are permitted to depend on both the current state
and a bounded number of future states of the chain. We show through several
examples that this added flexibility gives one a direct path to asymptotic
normality of the optimal total reward of finite horizon Markov decision
problems. The same examples also explain why such results are not easily
obtained by alternative Markovian techniques such as enlargement of the
state space. (Joint work with J. M. Steele.)