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

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.

22 pages, 10 figures, accepted by Journal of Physics A

References in corpus (3)

• Stochastic models which separate fractal dimension and Hurst effect
• Analytic Properties and Covariance Functions of a New Class of Generalized Gibbs Random Fields
• Spartan Random Processes in Time Series Modeling

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