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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...

Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model

Christophe Sabot, Pierre Tarrès (2015)

Journal of the European Mathematical Society

Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [8], is a random process which takes values in the vertex set of a graph G and is more likely to cross edges it has visited before. We show that it can be represented in terms of a vertex-reinforced jump process (VRJP) with independent gamma conductances; the VRJP was conceived by Werner and first studied by Davis and Volkov [10, 11], and is a continuous-time process favouring sites with more local time. We calculate,...

Efficiency of some algorithms for prediction in finite stationary time series

Pavel Ranocha (2004)

Kybernetika

Important characteristics of any algorithm are its complexity and speed in real calculations. From this point of view, we analyze some algorithms for prediction in finite stationary time series. First, we review results developed by P. Bondon [1] and then, we derive the complexities of Levinson and a new algorithm. It is shown that the time needed for real calculations of predictions is proportional to the theoretical complexity of the algorithm. Some practical recommendations for the selection...

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...

Elliptic gaussian random processes.

Albert Benassi, Stéphane Jaffard, Daniel Roux (1997)

Revista Matemática Iberoamericana

We study the Gaussian random fields indexed by Rd whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal symbol...

Elliptic self-similar stochastic processes.

Albert Benassi, Daniel Roux (2003)

Revista Matemática Iberoamericana

Let M be a random measure and L be an elliptic pseudo-differential operator on Rd. We study the solution of the stochastic problem LX = M, X(O) = O when some homogeneity and integrability conditions are assumed. If M is a Gaussian measure the process X belongs to the class of Elliptic Gaussian Processes which has already been studied. Here the law of M is not necessarily Gaussian. We characterize the solutions X which are self-similar and with stationary increments in terms of the driving mcasure...

Embedding of random vectors into continuous martingales

E. Dettweiler (1999)

Studia Mathematica

Let E be a real, separable Banach space and denote by L 0 ( Ω , E ) the space of all E-valued random vectors defined on the probability space Ω. The following result is proved. There exists an extension Ω ˜ of Ω, and a filtration ( ℱ ˜ t ) t ≥ 0 on Ω ˜ , such that for every X ∈ L 0 ( Ω , E ) there is an E-valued, continuous ( ℱ ˜ t ) -martingale ( M t ( X ) ) t ≥ 0 in which X is embedded in the sense that X = M τ ( X ) a.s. for an a.s. finite stopping time τ. For E = ℝ this gives a Skorokhod embedding for all X ∈ L 0 ( Ω , ℝ ) , and for general E this leads to a representation of random vectors as...

Enhanced Gaussian processes and applications

Laure Coutin, Nicolas Victoir (2009)

ESAIM: Probability and Statistics

We propose some construction of enhanced Gaussian processes using Karhunen-Loeve expansion. We obtain a characterization and some criterion of existence and uniqueness. Using rough-path theory, we derive some Wong-Zakai Theorem.

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