Approximating a harmonizable isotropic random field.
Swift, Randall J. (2001)
Journal of Applied Mathematics and Stochastic Analysis
Catherine Bouton (1988)
Annales de l'I.H.P. Probabilités et statistiques
Tan, Wai-Yuan, Ye, Zhengzheng (2000)
Journal of Theoretical Medicine
Tomáš Cipra (1994)
Applications of Mathematics
The problem of asymmetry appears in various aspects of time series modelling. Typical examples are asymmetric time series, asymmetric error distributions and asymmetric loss functions in estimating and predicting. The paper deals with asymmetric modifications of some recursive time series methods including Kalman filtering, exponential smoothing and recursive treatment of Box-Jenkins models.
A. Budhiraja (2003)
Annales de l'I.H.P. Probabilités et statistiques
Marina L. Kleptsyna, Alain Le Breton, Michel Viot (2004)
SORT
In this paper, the filtering problem is revisited in the basic Gaussian homogeneous linear system driven by fractional Brownian motions. We exhibit a simple approximate filter which is asymptotically optimal in the sense that, when the observation time tends to infinity, the variance of the corresponding filtering error converges to the same limit as for the exact optimal filter.
Pierre Del Moral, Laurent Miclo (2000)
Séminaire de probabilités de Strasbourg
Dan Crisan, Thomas G. Kurtz, Yoonjung Lee (2014)
Annales de l'I.H.P. Probabilités et statistiques
Stochastic partial differential equations (SPDEs) whose solutions are probability-measure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential equation,...
Aurélien Alfonsi, Antje Fruth, Alexander Schied (2008)
Banach Center Publications
We consider the problem of optimally placing market orders so as to minimize the expected liquidity costs from buying a given amount of shares. The liquidity price impact of market orders is described by an extension of a model for a limit order book with resilience that was proposed by Obizhaeva and Wang (2006). We extend their model by allowing for a time-dependent resilience rate, arbitrary trading times, and general equilibrium dynamics for the unaffected bid and ask prices. Our main results...
Buldygin, V.V., Koval, V.A. (2001)
Georgian Mathematical Journal
I. Kopocińska, B. Kopociński (2006)
Applicationes Mathematicae
We assume that the current score of a basketball game can be modeled by a bivariate cumulative process based on some marked renewal process. The basic element of a game is a cycle, which is concluded whenever a team scores. This paper deals with the joint probability distribution function of this cumulative process, the process describing the host's advantage and its expected value. The practical usefulness of the model is demonstrated by analyzing the effect of small modifications of the model...
Anton Bovier, Irina Kurkova (2004)
Annales de l'I.H.P. Probabilités et statistiques
Siegfried Graf, Harald Luschgy, Gilles Pagès (2008)
ESAIM: Probability and Statistics
We elucidate the asymptotics of the Ls-quantization error induced by a sequence of Lr-optimal n-quantizers of a probability distribution P on when s > r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s < r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on and on the Wiener space.
Alison M. Etheridge (2008)
Banach Center Publications
Understanding the evolution of individuals which live in a structured and fluctuating environment is of central importance in mathematical population genetics. Here we outline some of the mathematical challenges arising from modelling structured populations, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time models for the genealogical trees relating individuals in a sample from that population. In addition to classical...
Tomáš Cipra (1996)
Applications of Mathematics
In actuarial practice the credibility models must face the problem of outliers and missing observations. If using the -estimation principle from robust statistics in combination with Kalman filtering one obtains the solution of this problem that is acceptable in the numerical framework of the practical actuarial credibility. The credibility models are classified as static and dynamic in this paper and the shrinkage is used for the final ratemaking.
E. Pardoux (1981)
Annales scientifiques de l'Université de Clermont. Mathématiques
Rémi Léandre (1985)
Séminaire de probabilités de Strasbourg
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...
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...
Parthasarathy, P.R., Dietz, Klaus (2005)
International Journal of Mathematics and Mathematical Sciences