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Mat. Zametki, 1972, Volume 12, Issue 4, Pages 443–451 (Mi mz9903)  

Compactness of probability measures and the uniform convergence of certain stochastic series

V. V. Buldygin

Kiev State University

Abstract: We give the conditions which ensure the compactness of the probability measures $\mu_n$, $n\geqslant1$, generated by Gaussian processes the realizations of which are continuous with unit probability in $[0, 1]$. We also give the conditions for the uniform convergence of stochastic series of the form $\sum_{k=1}^\infty\xi_k(t)$, where the $\xi_k(t)$ are independent Gaussian processes the realizations of which are continuous with unit probability in $[0, 1]$.

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English version:
Mathematical Notes, 1972, 12:4, 699–704

Bibliographic databases:

UDC: 519.2
Received: 16.03.1971

Citation: V. V. Buldygin, “Compactness of probability measures and the uniform convergence of certain stochastic series”, Mat. Zametki, 12:4 (1972), 443–451; Math. Notes, 12:4 (1972), 699–704

Citation in format AMSBIB
\Bibitem{Bul72}
\by V.~V.~Buldygin
\paper Compactness of probability measures and the uniform convergence of certain stochastic series
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 4
\pages 443--451
\mathnet{http://mi.mathnet.ru/mz9903}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=346864}
\zmath{https://zbmath.org/?q=an:0249.60028}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 4
\pages 699--704
\crossref{https://doi.org/10.1007/BF01093677}


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