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

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