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Ecuaciones de la descomposición modal de procesos ARMA.

Juan José Egozcue Rubí, Eulàlia Griful Ponsati (1987)

Stochastica

Los procesos estocásticos estacionarios, autorregresivos y de medias móviles (ARMA), han sido estudiados en diversos ámbitos durante las dos últimas décadas (p.e. Brockwell-Davis, 1987), y se han utilizado con éxito en aplicaciones muy diversas.Uno de los aspectos al que parece que no se ha prestado demasiada atención es la descomposición aditiva de estos procesos, asociando cada componente a un polo de la función de transferencia del modelo ARMA. Esta descomposición aditiva, que llamaremos descomposición...

Efficient measurement of higher-order statistics of stochastic processes

Wladyslaw Magiera, Urszula Libal, Agnieszka Wielgus (2018)

Kybernetika

This paper is devoted to analysis of block multi-indexed higher-order covariance matrices, which can be used for the least-squares estimation problem. The formulation of linear and nonlinear least squares estimation problems is proposed, showing that their statements and solutions lead to generalized `normal equations', employing covariance matrices of the underlying processes. Then, we provide a class of efficient algorithms to estimate higher-order statistics (generalized multi-indexed covariance...

Epsilon-independence between two processes

Tomasz Downarowicz, Paulina Grzegorek (2008)

Studia Mathematica

We study the notion of ε-independence of a process on finitely (or countably) many states and that of ε-independence between two processes defined on the same measure preserving transformation. For that we use the language of entropy. First we demonstrate that if a process is ε-independent then its ε-independence from another process can be verified using a simplified condition. The main direction of our study is to find natural examples of ε-independence. In case of ε-independence of one process,...

Ergodicity of hypoelliptic SDEs driven by fractional brownian motion

M. Hairer, N. S. Pillai (2011)

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

We demonstrate that stochastic differential equations (SDEs) driven by fractional brownian motion with Hurst parameter H>½ have similar ergodic properties as SDEs driven by standard brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’s condition. We show that such systems enjoy a suitable version of the strong Feller property and we conclude that under a standard controllability condition they admit a unique stationary solution that is physical in the...

Estimating an even spherical measure from its sine transform

Lars Michael Hoffmann (2009)

Applications of Mathematics

To reconstruct an even Borel measure on the unit sphere from finitely many values of its sine transform a least square estimator is proposed. Applying results by Gardner, Kiderlen and Milanfar we estimate its rate of convergence and prove strong consistency. We close this paper by giving an estimator for the directional distribution of certain three-dimensional stationary Poisson processes of convex cylinders which have applications in material science.

Estimating the conditional expectations for continuous time stationary processes

Gusztáv Morvai, Benjamin Weiss (2020)

Kybernetika

One of the basic estimation problems for continuous time stationary processes X t , is that of estimating E { X t + β | X s : s ∈ [ 0 , t ] } based on the observation of the single block { X s : s ∈ [ 0 , t ] } when the actual distribution of the process is not known. We will give fairly optimal universal estimates of this type that correspond to the optimal results in the case of discrete time processes.

Estimation of anisotropic gaussian fields through Radon transform

Hermine Biermé, Frédéric Richard (2008)

ESAIM: Probability and Statistics

We estimate the anisotropic index of an anisotropic fractional brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional brownian field and prove that these processes admit...

Estimation of anisotropic Gaussian fields through Radon transform

Hermine Biermé, Frédéric Richard (2007)

ESAIM: Probability and Statistics

We estimate the anisotropic index of an anisotropic fractional Brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional Brownian field and prove that these processes...

Estimation of the spectral moment by means of the extrema.

Enrique M. Cabaña (1985)

Trabajos de Estadística e Investigación Operativa

An estimator of the standard deviation of the first derivative of a stationary Gaussian process with known variance and two continuous derivatives, based on the values of the relative maxima and minima, is proposed, and some of its properties are considered.

Excursions of the integral of the brownian motion

Emmanuel Jacob (2010)

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

The integrated brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a stationary Langevin process and then determine explicitly its stationary excursion measure. This is then used to provide new descriptions of Itô’s excursion measure of the Langevin process reflected at a completely inelastic boundary, which has been...

Extremes in multivariate stationary normal sequences

Mateusz Wiśniewski (1998)

Applicationes Mathematicae

This paper deals with a weak convergence of maximum vectors built on the base of stationary and normal sequences of relatively strongly dependent random vectors. The discussion concentrates on the normality of limits and extends some results of McCormick and Mittal [4] to the multivariate case.

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