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Adaptive density estimation under weak dependence

Irène Gannaz, Olivier Wintenberger (2010)

ESAIM: Probability and Statistics

Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue's measure. [Donoho et al. Ann. Stat.24 (1996) 508–539] propose near-minimax estimators f ^ n based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim of the present work is to extend these results to general weak dependent contexts. Weak dependence assumptions are expressed as decreasing bounds of covariance terms and are...

Adaptive estimation of the conditional intensity of marker-dependent counting processes

F. Comte, S. Gaïffas, A. Guilloux (2011)

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

We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a nonasymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly, we provide...

Adaptive wavelet estimation of the diffusion coefficient under additive error measurements

M. Hoffmann, A. Munk, J. Schmidt-Hieber (2012)

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

We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular in high frequency financial data modelling, however mainly from a parametric and semiparametric point of view. This paper addresses the nonparametric estimation of the path of the (possibly stochastic) diffusion coefficient in a relatively general setting. By...

Additive Covariance kernels for high-dimensional Gaussian Process modeling

Nicolas Durrande, David Ginsbourger, Olivier Roustant (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

Gaussian Process models are often used for predicting and approximating expensive experiments. However, the number of observations required for building such models may become unrealistic when the input dimension increases. In oder to avoid the curse of dimensionality, a popular approach in multivariate smoothing is to make simplifying assumptions like additivity. The ambition of the present work is to give an insight into a family of covariance kernels that allows combining the features of Gaussian...

Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime

Nathanaël Enriquez, Christophe Sabot, Olivier Zindy (2009)

Bulletin de la Société Mathématique de France

We consider transient one-dimensional random walks in a random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of “valleys“ of height log t . In the quenched setting, we also sharply estimate the distribution of the walk at time t .

Almost automorphic solution for some stochastic evolution equation driven by Lévy noise with coefficients S2−almost automorphic

Mamadou Moustapha Mbaye (2016)

Nonautonomous Dynamical Systems

In this work we first introduce the concept of Poisson Stepanov-like almost automorphic (Poisson S2−almost automorphic) processes in distribution. We establish some interesting results on the functional space of such processes like an composition theorems. Next, under some suitable assumptions, we establish the existence, the uniqueness and the stability of the square-mean almost automorphic solutions in distribution to a class of abstract stochastic evolution equations driven by Lévy noise in case...

Almost everywhere convergence of convolution powers on compact abelian groups

Jean-Pierre Conze, Michael Lin (2013)

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

It is well-known that a probability measure μ on the circle 𝕋 satisfies ∥ μ n * f - ∫ f d m ∥ p → 0 for every f ∈ L p , every (some) p ∈ [ 1 , ∞ ) , if and only if | μ ^ ( n ) | l t ; 1 for every non-zero n ∈ ℤ ( μ is strictly aperiodic). In this paper we study the a.e. convergence of μ n * f for every f ∈ L p whenever p g t ; 1 . We prove a necessary and sufficient condition, in terms of the Fourier–Stieltjes coefficients of μ , for the strong sweeping out property (existence of a Borel set B with lim sup μ n * 1 B = 1 a.e. and lim inf μ n * 1 B = 0 a.e.). The results are extended to general compact Abelian groups G with Haar...

Almost log-optimal trading strategies for small transaction costs in model with stochastic coefficients

Petr Dostál (2022)

Kybernetika

We consider a non-consuming agent investing in a stock and a money market interested in the portfolio market price far in the future. We derive a strategy which is almost log-optimal in the long run in the presence of small proportional transaction costs for the case when the rate of return and the volatility of the stock market price are bounded It o processes with bounded coefficients and when the volatility is bounded away from zero.

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