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

Eva Löcherbach, Dasha Loukianova, Oleg Loukianov (2011)

ESAIM: Probability and Statistics

Let X be a one dimensional positive recurrent diffusion continuously observed on [0,t] . 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 t → ∞. The main point of our work is that we do not suppose the process to be in...

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

Eva Löcherbach, Dasha Loukianova, Oleg Loukianov (2012)

ESAIM: Probability and Statistics

Let X be a one dimensional positive recurrent diffusion continuously observed on [0,t] . 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 t → ∞. The main point of our work is that we do not suppose the process to be in...

Persistence and extinction of a stochastic delay predator-prey model under regime switching

Zhen Hai Liu, Qun Liu (2014)

Applications of Mathematics

The paper is concerned with a stochastic delay predator-prey model under regime switching. Sufficient conditions for extinction and non-persistence in the mean of the system are established. The threshold between persistence and extinction is also obtained for each population. Some numerical simulations are introduced to support our main results.

Perturbation de générateurs infinitésimaux du type «changement de temps»

Gunter Lumer (1973)

Annales de l'institut Fourier

On obtient un théorème général concernant la perturbation multiplicative par un opérateur (linéaire borné, mais pas forcément d’inverse borné), du générateur d’un semi-groupe fortement continu sur un espace de Banach. On en déduit un résultat intimement lié au changement de temps dans les processus de Markov, qui étend un théorème de Dorroh (et résout par l’affirmative la seule situation qui restait en doute dans le contexte du théorème de Dorroh cité). Comme exemple d’autres possibilités d’application,...

Perturbation of analytic operators and temporal regularity of discrete heat kernels

Sönke Blunck (2000)

Colloquium Mathematicae

In analogy to the analyticity condition ∥ A e t A ∥ ≤ C t - 1 , t > 0, for a continuous time semigroup ( e t A ) t ≥ 0 , a bounded operator T is called analytic if the discrete time semigroup ( T n ) n ∈ ℕ satisfies ∥ ( T - I ) T n ∥ ≤ C n - 1 , n ∈ ℕ. We generalize O. Nevanlinna’s characterization of powerbounded and analytic operators T to the following perturbation result: if S is a perturbation of T such that ∥ R ( λ 0 , T ) - R ( λ 0 , S ) ∥ is small enough for some λ 0 ∈ ϱ ( T ) ∩ ϱ ( S ) , then the type ω of the semigroup ( e t ( S - I ) ) also controls the analyticity of S in the sense that ∥ ( S - I ) S n ∥ ≤ C ( ω + n - 1 ) e ω n , n ∈ ℕ. As an application we generalize...

Currently displaying 21 – 40 of 149