Cassim, A.; Ivković, Z. Multidimensional Hermite polynomials of complex Gaussian variables. (English) Zbl 0830.60031 Publ. Inst. Math., Nouv. Sér. 55(69), 146-148 (1994). Multidimensional Hermite polynomials of complex Gaussian variables are defined and some properties are investigated. Let \(\{Z(t), t \in R^d\}\) be a complex-valued second-order Gaussian random field. Then \[ E \bigl( Z(t) \mid Z(s) \bigr) = Z (s \wedge t) \quad \text{and} \quad \biggl \langle H_p \bigl( Z(s) \bigr),\;H_p \bigl( Z(t) \bigr) \biggr \rangle = \biggl |H_p \bigl( Z(s \wedge t) \bigr) \biggr |^2, \] where \(H_p\) is a one-dimensional Hermite polynomial. Reviewer: N.Leonenko (Kiev) MSC: 60G15 Gaussian processes 62M40 Random fields; image analysis Keywords:orthogonal random fields; multidimensional Hermite polynomials; complex Gaussian variables PDFBibTeX XMLCite \textit{A. Cassim} and \textit{Z. Ivković}, Publ. Inst. Math., Nouv. Sér. 55(69), 146--148 (1994; Zbl 0830.60031) Full Text: EuDML EMIS