Polynomial bounds in the Ergodic theorem for one-dimensional diffusions and integrability of hitting times
Eva Löcherbach, Dasha Loukianova, Oleg Loukianov (2011)
Annales de l'I.H.P. Probabilités et statistiques
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Let be a one-dimensional positive recurrent diffusion with initial distribution and invariant probability . Suppose that for some >1, ∈ℝ such that ∀∈ℝ, and , where is the hitting time of . For such a diffusion, we derive non-asymptotic deviation bounds of the form ℙ(|(1/)0 ( ) d−()|≥)≤()(1/ /2)(1/ )(). Here bounded or bounded and compactly supported and ()=‖‖∞ when is bounded and ()=(||) when is...