Currently displaying 1 – 7 of 7

Showing per page

Order by Relevance | Title | Year of publication

Polynomial deviation bounds for recurrent Harris processes having general state space

Eva LöcherbachDasha Loukianova — 2013

ESAIM: Probability and Statistics

Consider a strong Markov process in continuous time, taking values in some Polish state space. Recently, Douc et al. [Stoc. Proc. Appl. 119, (2009) 897–923] introduced verifiable conditions in terms of a supermartingale property implying an explicit control of modulated moments of hitting times. We show how this control can be translated into a control of polynomial moments of abstract regeneration times which are obtained by using the regeneration...

Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process

Eva LöcherbachDasha LoukianovaOleg Loukianov — 2011

ESAIM: Probability and Statistics

Let be a one dimensional positive recurrent diffusion continuously observed on [0,] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when → ∞. The main point of our work is that we do not suppose the process to be in stationary...

Polynomial bounds in the Ergodic theorem for one-dimensional diffusions and integrability of hitting times

Eva LöcherbachDasha LoukianovaOleg Loukianov — 2011

Annales de l'I.H.P. Probabilités et statistiques

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 bounded and...

Spectral condition, hitting times and Nash inequality

Eva LöcherbachOleg LoukianovDasha Loukianova — 2014

Annales de l'I.H.P. Probabilités et statistiques

Let X be a μ -symmetric Hunt process on a LCCB space 𝙴 . For an open set 𝙶 𝙴 , let τ 𝙶 be the exit time of X from 𝙶 and A 𝙶 be the generator of the process killed when it leaves 𝙶 . Let r : [ 0 , [ [ 0 , [ and R ( t ) = 0 t r ( s ) d s . We give necessary and sufficient conditions for 𝔼 μ R ( τ 𝙶 ) l t ; in terms of the behavior near the origin of the spectral measure of - A 𝙶 . When r ( t ) = t l , l 0 , by means of this condition we derive the Nash inequality for the killed process. In the diffusion case this permits to show that the existence of moments of order l + 1 for τ 𝙶 implies the...

Penalized nonparametric drift estimation for a continuously observed one-dimensional diffusion process

Eva LöcherbachDasha LoukianovaOleg Loukianov — 2012

ESAIM: Probability and Statistics

Let be a one dimensional positive recurrent diffusion continuously observed on [0,] . We consider a non parametric estimator of the drift function on a given interval. Our estimator, obtained using a penalized least square approach, belongs to a finite dimensional functional space, whose dimension is selected according to the data. The non-asymptotic risk-bound reaches the minimax optimal rate of convergence when → ∞. The main point of our work is that we do not suppose the process to be in stationary...

Page 1

Download Results (CSV)