Yurachkivs’kyj, A. P. Covariation-characteristic functions of random measures and their applications to stochastic geometry. (English) Zbl 0962.60034 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1999, No. 5, 49-54 (1999). Let \(\mathcal G\) be the space, endowed with weak topology, of all probability measures on the \(\sigma\)-algebra of Borel sets \({\mathcal B}^{d}\) in \({\mathbb R}^{d}\). Then a random measure \(\psi\) on \({\mathcal B}^{d}\) is a \(\mathcal G\)-valued random element. The covariation-characteristic function of the random measure \(\psi\) is defined as \[ E\int\dots\int\exp\{i(z_1 x_1+\dots+z_{n}x_{n})\}\psi(dx_1)\dots \psi(dx_{n}), \quad n\in{\mathbb N},\;z_{j}\in {\mathbb R}^{d}. \] One-to-one correspondence between the distribution of random measures \(\psi\) and their characteristic functions is proved. Applications to random measures generated by random fields are proposed. Reviewer: M.P.Moklyachuk (Kyïv) Cited in 2 Reviews MSC: 60G57 Random measures Keywords:random measure; covariation-characteristic function; distribution PDFBibTeX XMLCite \textit{A. P. Yurachkivs'kyj}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1999, No. 5, 49--54 (1999; Zbl 0962.60034)