ESTIMATION OF SAMPLE SPACING IN STOCHASTIC PROCESSES

Motivated by applications in electron microscopy, we study the situation where a stationary and isotropic random field is observed on two parallel planes with unknown distance. We propose an estimator for this distance. Under the tractable, yet flexible class of Lévy-based random field models, we derive an approximate variance of the estimator. The estimator and the approximate variance perform well in two simulation studies.

A new criterion for testing hypothesis about the covariance function of the homogeneous and isotropic random field

In this paper, we consider a continuous in mean square homogeneous and isotropic Gaussian random field. A criterion for testing hypotheses about the covariance function of such field using estimates for its norm in the space $L_p(\mathbb{T}), p\geq 1$ is constructed.

Approximating a harmonizable isotropic random field

The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers a stochastic series approximation of a harmonizable isotropic random field. This approximation is useful for numerical simulation of such a field.

A strong law of large numbers for harmonizable isotropic random fields

The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers a strong law of large numbers for the spherical average of a harmonizable isotropic random field.