Concentration Inequalities for Markov Jump Processes
Abstract
We derive concentration inequalities for empirical means 1t ∫0t f(Xs) ds where Xs is an irreducible Markov jump process on a finite state space and f some observable. Using a Feynman-Kac semigroup we first derive a general concentration inequality. Then, based on this inequality we derive further concentration inequalities. Hereby we use three different methods; perturbation theory, Poincar\'e inequalities and information inequalities. We also obtain a Bernstein type concentration inequality.
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