RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 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 $[0, 1]$.

Full text: PDF file (819 kB)

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

Bibliographic databases:

UDC: 519.2

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}