Stationary Fourier hyperprocesses
This is an application of the theory of vector valued Fourier hyperfunctions. In this paper, the author defined a concept of stationary Fourier hyperprocesses and studied their properties. A random Fourier hyperprocess is defined to be a vector valued Fourier hyperfunction on \({\mathbb{D}}=[-\infty,\infty]\) whose values are random variables with mean 0 and finite variance. Then he defined a concept of stationary (random) Fourier hyperprocesses. At first, he showed the existence of the covariance Fourier hyperfunction of a stationary Fourier hyperprocess. Next, he showed that this covariance Fourier hyperfunction \(\rho\) is the Fourier transform of a nonnegative measure \(\mu\) with infraexponential increase. This measure \(\mu\) is called the spectral measure of \(\rho\). At last he proved that any stationary Fourier hyperprocess is the Fourier transform of a random hypomeasure with respect to the spectral measure of its covariance Fourier hyperfunction. Here we note that Theorem 3.3 and Theorem 3.5 should be omitted because its assertions are incorrect.
scientific article; zbMATH DE number 3976005