Moyennes et mesures en mécanique quantique et en mécanique classique
Multidimensional random processes with normal covariances
-аппроксимация функции правдоподобия
Non-negative linear processes
Conditions under which the linear process is non-negative are investigated in the paper. In the definition of the linear process a strict white noise is used. Explicit results are presented also for the models AR(1) and AR(2).
Nonparametric estimation of the derivatives of the stationary density for stationary processes
In this article, our aim is to estimate the successive derivatives of the stationary density f of a strictly stationary and β-mixing process (Xt)t≥0. This process is observed at discrete times t = 0,Δ,...,nΔ. The sampling interval Δ can be fixed or small. We use a penalized least-square approach to compute adaptive estimators. If the derivative f(j)belongs to the Besov space B 2 , ∞ α , then our estimator converges at rate (nΔ)−α/(2α+2j+1). Then we consider a diffusion with known diffusion coefficient....
Normal covariances
Note on the central limit theorem for stationary processes
On a class of estimators in a multivariate RCA(1) model
This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...
On a Martingale Related to a Strictly Stationary Random Process in R1.
On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields *
Many statistical applications require establishing central limit theorems for sums/integrals or for quadratic forms , where Xt is a stationary process. A particularly important case is that of Appell polynomials h(Xt) = Pm(Xt), h(Xt,Xs) = Pm,n (Xt,Xs), since the “Appell expansion rank" determines typically the type of central limit theorem satisfied by the functionals ST(h), QT(h). We review and extend here to multidimensional indices, along lines conjectured in [F. Avram and M.S. Taqqu,...
On calculation of stationary density of autoregressive processes
An iterative procedure for computation of stationary density of autoregressive processes is proposed. On an example with exponentially distributed white noise it is demonstrated that the procedure converges geometrically fast. The AR(1) and AR(2) models are analyzed in detail.
On characterizations of interpolable and minimal stationary processes
On Covariance Of Spectral Estimates Of Stationary Random Sequence
On estimates of mean values of random AR-fields.
On estimating the memory for finitarily markovian processes
On Extrapolation of Moving Average and Autoregressive Processes
On interpolation of moving average processes
On invertibility of a random coefficient moving average model
A linear moving average model with random coefficients (RCMA) is proposed as more general alternative to usual linear MA models. The basic properties of this model are obtained. Although some model properties are similar to linear case the RCMA model class is too general to find general invertibility conditions. The invertibility of some special examples of RCMA(1) model are investigated in this paper.
On Marginal Distributions and Isomorphisms of Stationary Processes.
On Markovian traffic with applications to TES processes.