Concentration of Additive Functionals for Markov Processes and Applications to Interacting Particle Systems

Details Concentration of Additive Functionals for Markov Processes and Applications to Interacting Particle Systems Concentration of Additive Functionals for Markov Processes and Applications to Interacting Particle Systems

2010-02-26

arxiv.org/abs/1003.0006v2

Mathematics

Probability

Scientific paper

We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions, interacting particle systems and random walks. In particular, for the symmetric exclusion process we generalize large deviation bounds for occupation times to general local functions. The method is based on coupling estimates and not spectral theory, hence reversibility is not needed. We bound the exponential moments(or the moments of finite order) in terms of a so-called coupled function difference, which in turn is estimated using the generalized coupling time. Along the way we prove a general relation between the contractivity of the semigroup and bounds on the generalized coupling time.

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