Large deviations for occupation times of Markov processes with $L_{\mathbf{2}}$ semigroups

Details Large deviations for occupation times of Markov processes with $L_{\mathbf{2}}$ semigroups Large deviations for occupation times of Markov processes with $L_{\mathbf{2}}$ semigroups

2007-07-30

arxiv.org/abs/0707.4469v2

Annals of Probability 2008, Vol. 36, No. 5, 1611-1641

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP371 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP371

Our aim is to unify and extend the large deviation upper and lower bounds for the occupation times of a Markov process with $L_2$ semigroups under minimal conditions on the state space and the process trajectories; for example, no strong Markov property is needed. The methods used here apply in both continuous and discrete time. We present the proofs for continuous time only because of the inherent technical difficulties in that situation; the proofs can be adapted for discrete time in a straightforward manner.

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