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We consider additive functionals of Markov processes in continuous time withgeneral (metric) state spaces. We derive concentration bounds for theirexponential moments and moments of finite order. Applications includediffusions, interacting particle systems and random walks. The method is basedon coupling estimates and not spectral theory, hence reversibility is notneeded. We bound the exponential moments(or the moments of finite order) interms of a so-called coupled function difference, which in turn is estimatedusing the generalized coupling time. Along the way we prove a general relationbetween the contractivity of the semigroup and bounds on the generalizedcoupling time.

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