Abstract:
The paper deals with different properties of generalized random fields, i.e. probability measures in spaces of linear functionals on linear topological spaces. A general construction is given which describes random variables depending on the field with the help of polynomials of the field. By using this construction, it is proved that the existence of moments of linear random functions implies continuity of their moment forms.
Citation:
R. L. Dobrušin, R. A. Minlos, “Polynomials of generalized random field and its moments”, Teor. Veroyatnost. i Primenen., 23:4 (1978), 715–730; Theory Probab. Appl., 23:4 (1979), 686–699
\Bibitem{DobMin78}
\by R.~L.~Dobru{\v s}in, R.~A.~Minlos
\paper Polynomials of generalized random field and its moments
\jour Teor. Veroyatnost. i Primenen.
\yr 1978
\vol 23
\issue 4
\pages 715--730
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=516270}
\zmath{https://zbmath.org/?q=an:0422.60044|0405.60054}
\transl
\jour Theory Probab. Appl.
\yr 1979
\vol 23
\issue 4
\pages 686--699
\crossref{https://doi.org/10.1137/1123086}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1978JA77700002}
Linking options:
https://www.mathnet.ru/eng/tvp3107
https://www.mathnet.ru/eng/tvp/v23/i4/p715
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Hans Zessin, “On the asymptotic behaviour of the free gas and its fluctuations in the hydrodynamical limit”, Probab. Th. Rel. Fields, 77:4 (1988), 605
Torbj�rn Kolsrud, “Gaussian random fields, infinite dimensional Ornstein-Uhlenbeck processes, and symmetric Markov processes”, Acta Appl Math, 12:3 (1988), 237
E. Bruning, Lecture Notes in Mathematics, 1250, Stochastic Processes — Mathematics and Physics II, 1987, 14
Hans Zessin, Stochastic Space—Time Models and Limit Theorems, 1985, 249
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