First of all,thank you for your help! I have some questions about structure function in Stochastic processes and random field.
Based on the definition of structure function in Stochastic processes and random field, the formula can be written as:$$D_F=\lt[F(\vec x_1, t_1 )-F(\vec x_2,t_1+T)]^2 \gt$$ Where $F(\vec x, t )$ is the random function.Now,the formula of the random function is:$$F(\vec r, t )=A(\vec r)\times e^{jwt}$$
Where $\vec r$ represents the Space vector,$w$ is constant,$j$ is imaginary unit,$t$ represents time.Note,$A(\vec r)$is merely relate to the Space vector $\vec r$.$e^{jwt}$ is a function of variable $t$.
The problem:Could $F(\vec r, t )$ be called a random function?If $F(\vec r, t )$ above mentioned is a random function,how to solve the structure function of the random function$F(\vec r, t )$ ?