Equivalence of measures and asymptotically optimal linear prediction for Gaussian random fields with fractional-order covariance operators

Incorporating covariance estimation uncertainty in spatial sampling design for prediction with trans-Gaussian random fields

Recently, Spöck and Pilz (2010), demonstrated that the spatial sampling design problem for the Bayesian linear kriging predictor can be transformed to an equivalent experimental design problem for a linear regression model with stochastic regression coefficients and uncorrelated errors. The stochastic regression coefficients derive from the polar spectral approximation of the residual process. ...

Autoregressive Gaussian Random Vectors of First Order

Optimal Non-Parametric Prediction Intervals for Order Statistics with Random Sample Size

‎ In many experiments, such as biology and quality control problems, sample size cannot always be considered as a constant value. Therefore, the problem of predicting future data when the sample size is an integer-valued random variable can be an important issue. This paper describes the prediction problem of future order statistics based on upper and lower records. Two different cases for the ...

Asymptotically optimal filtering in linear systems with fractional Brownian noises

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.

Gaussian Fields and Gaussian Sheets with Generalized Cauchy Covariance Structure

Abstract. Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic properties of the spectral densities of these random fields are studied. The associated self-similar random fields obtained by applying the Lamperti transf...