Generalized Whittle-Mat$\acute{\text{E}}$rn random field as a model of correlated fluctuations

TL;DR

This paper introduces a generalized Whittle-Matérn Gaussian random field model, derived from fractional stochastic differential equations, offering enhanced flexibility for modeling correlated geostatistical data like wind speed.

Contribution

It extends the classical Whittle-Matérn model by incorporating fractional orders, analyzing its asymptotic covariance properties, and demonstrating its improved applicability to wind speed data.

Findings

Generalized model captures more complex spatial correlations.

Asymptotic covariance properties are characterized.

Enhanced fit to wind speed data compared to classical models.

Abstract

This paper considers a generalization of Gaussian random field with covariance function of Whittle-Mat$\acute{\text{e}}$rn family. Such a random field can be obtained as the solution to the fractional stochastic differential equation with two fractional orders. Asymptotic properties of the covariance functions belonging to this generalized Whittle-Mat$\acute{\text{e}}$rn family are studied, which are used to deduce the sample path properties of the random field. The Whittle-Mat$\acute{\text{e}}$rn field has been widely used in modeling geostatistical data such as sea beam data, wind speed, field temperature and soil data. In this article we show that generalized Whittle-Mat$\acute{\text{e}}$rn field provides a more flexible model for wind speed data.