MODERATE DEVIATION PRINCIPLE FOR ERGODIC MARKOV CHAIN. LIPSCHITZ SUMMANDS

by R. Lipster

Institution: Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv Israel
Date: Thu 17th March 2005
Time: 1:15 PM
Location: Room 213, Richard Berry Building

Abstract: For 1
2 < < 1, we propose the MDP analysis for family
S
n =
1
n
n Xi=1
H(XiÃ…|1), n 1,
where (Xn)n 0 be a homogeneous ergodic Markov chain, Xn 2 Rd,
when the spectrum of operator Px is continuous. The vector-valued
function H is not assumed to be bounded but the Lipschitz continuity
of H is required. The main helpful tools in our approach are Poissonâ€™s
equation and Stochastic Exponential; the first enables to replace the
original family by 1
n Mn with a martingale Mn while the second to
avoid the direct Laplace transform analysis.