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Euclidean random fields obtained by convolution from generalized white noise. (English) Zbl 0841.60091

Summary: We study Euclidean random fields \(X\) over \(\mathbb{R}^d\) of the form \(X = G * F\), where \(F\) is a generalized white noise over \(\mathbb{R}^d\) and \(G\) is an integral kernel. We give conditions for the existence of the characteristic functional and moment functions and we construct a convergent lattice approximation of \(X\). Finally, we perform the analytic continuation of the moment functions and the characteristic functional of \(X\), obtaining the corresponding relativistic functions on Minkowski space.

MSC:

60K40 Other physical applications of random processes
83C99 General relativity
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