A complete description of anisotropic scaling limits and the existence of scaling transition for nonlinear functions (Appell polynomials) of stationary linear random fields on with moving average coefficients decaying at possibly different rate in the horizontal and the vertical direction is obtained.
A characterization of what characteristic functions of a probability measures are uniquely determined by their imaginary parts is given. The conditions under which, for a neighbourhood U of infinity and a characteristic function F on U, there exists an uniquely extension of F to the whole line also are investigated.
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