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- W2090916000 abstract "Let X be a Harris recurrent strong Markov process in continuous time with general Polish state space E, having invariant measure μ. In this paper we use the regeneration method to derive non asymptotic deviation bounds for $$P_{x}biggl(biggl|int_0^tf(X_s),dsbiggr|geq t^{frac{1}{2}+eta}varepsilon biggr)$$in the positive recurrent case, for nice functions f with μ(f)=0 (f must be a charge). We generalize these bounds to the fully null-recurrent case in the moderate deviations regime. We obtain a Gaussian concentration bound for all functions f which are a charge. The rate of convergence is expressed in terms of the deterministic equivalent of the process. The main ingredient of the proof is Nummelin splitting in continuous time, which allows one to introduce regeneration times for the process on an enlarged state space." @default.
- W2090916000 created "2016-06-24" @default.
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- W2090916000 date "2010-09-17" @default.
- W2090916000 modified "2023-10-14" @default.
- W2090916000 title "Deviation Inequalities for Centered Additive Functionals of Recurrent Harris Processes Having General State Space" @default.
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- W2090916000 doi "https://doi.org/10.1007/s10959-010-0310-y" @default.
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