具有一般国家空间的哈里斯进程重复出现的核心添加添加剂功能的偏差不平等 (Deviation inequalities for centered additive functionals of recurrent Harris processes having general state space)

Let $X$ be a Harris recurrent strong Markov process in continuous time with general Polish state space $E,$ having invariant measure $\mu .$ In this paper we use the regeneration method to derive non asymptotic deviation bounds for $$P_{x} (|\int_0^tf(X_s)ds|\geq t^{\frac12 + \eta} \ge)$$ in the positive recurrent case, for nice functions $f$ with $\mu (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 contentration 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 to introduce regeneration times for the process on an enlarged state space.

翻译：在波兰国家通用空间连续使用时,让我们用美元作为Harris经常的坚固的马可夫程序, 美元, 美元, 美元, 美元, 美元, 美元。在本文件中, 我们使用再生法来得出美元P ⁇ x}( ⁇ int_ 0 ⁇ tf( X_)ds ⁇ geq t ⁇ z ⁇ frac12 +\eta} ge) 美元的非非非无损偏差边框。在正常情况下, 证据的主要成分是 Nummelin, 持续地分解, 从而可以对扩大的国家空间的进程引入再生时间。