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Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 3, Pages 536–541 (Mi tvp2664)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

The action functional for a class of stochastic processes

M. I. Freidlin

Moscow

Abstract: Let $x_t$ be a Gaussian process with zero mean and correlation operator $A$. The action functional for this process is defined by the equality $S(\varphi)=(A^{-1/2}\varphi,A^{-1/2}\varphi)$. We prove a number of theorems concerning action functionals which enable us to solve some asymptotic problems for Gaussian processes and processes obtained from Gaussian ones by nonlinear transforms.

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English version:
Theory of Probability and its Applications, 1973, 17:3, 511–515

Bibliographic databases:

Received: 18.11.1970

Citation: M. I. Freidlin, “The action functional for a class of stochastic processes”, Teor. Veroyatnost. i Primenen., 17:3 (1972), 536–541; Theory Probab. Appl., 17:3 (1973), 511–515

Citation in format AMSBIB
\Bibitem{Fre72}
\by M.~I.~Freidlin
\paper The action functional for a~class of stochastic processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 3
\pages 536--541
\mathnet{http://mi.mathnet.ru/tvp2664}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=307314}
\zmath{https://zbmath.org/?q=an:0268.60040}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 17
\issue 3
\pages 511--515
\crossref{https://doi.org/10.1137/1117059}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. I. Kifer, “On small random perturbations of some smooth dynamical systems”, Math. USSR-Izv., 8:5 (1974), 1083–1107  mathnet  crossref  mathscinet
    2. M. I. Freidlin, “The averaging principle and theorems on large deviations”, Russian Math. Surveys, 33:5 (1978), 117–176  mathnet  crossref  mathscinet  zmath
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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