On the integral with respect to the tensor product of two random measures

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On the integral with respect to the tensor product of two random measures

A Fubini-type formula for the integral with respect to the tensor product of two random measures is established in an intrinsic way. This permits one to consider a convolution product. The results are applied to a stationary continuous random function (which may be multiplicatively written with two stationary components) and to principal component analysis in the frequency domain.Convolution of measures Fubini-type formula Locally compact Abelian group Random measure Spectral density Spectral measure Stationary random function stochastic integral Tensor product