Itogi Nauki i Tekhniki. Seriya "Teoriya Veroyatnostei. Matematicheskaya Statistika. Teoreticheskaya Kibernetika"
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Itogi Nauki i Tekhniki. Seriya "Teoriya Veroyatnostei. Matematicheskaya Statistika. Teoreticheskaya Kibernetika", 1990, Volume 27, Pages 79–128 (Mi intv73)  
This article is cited in 2 scientific papers (total in 2 papers)

Stability of infinite systems of stochastic equations

I. A. Ignatyuk, V. A. Malyshev, T. S. Turova
Full-text PDF (1839 kB) Citations (2)
Abstract: A study is presented of processes with local interaction and infinite systems of Itô equations, which are small perturbations of independent processes at each point of a lattice with noncompact set of values. A survey of results and a complete exposition are devoted to the technique of cluster expansions, which uses estimates of the Lyapunov function type. This technique permits total control over the temporal evolution of the system and, in particular, enables one to prove that the temporal evolution is exponentially convergent.
English version:
Journal of Soviet Mathematics, 1992, Volume 61, Issue 3, Pages 2114–2151
DOI: https://doi.org/10.1007/BF01097527
Bibliographic databases:
UDC: 519.248
Language: Russian
Citation: I. A. Ignatyuk, V. A. Malyshev, T. S. Turova, “Stability of infinite systems of stochastic equations”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 27, VINITI, Moscow, 1990, 79–128; J. Soviet Math., 61:3 (1992), 2114–2151
Citation in format AMSBIB
\Bibitem{IgnMalTur90}
\by I.~A.~Ignatyuk, V.~A.~Malyshev, T.~S.~Turova
\paper Stability of infinite systems of stochastic equations
\serial Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern.
\yr 1990
\vol 27
\pages 79--128
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intv73}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1067162}
\zmath{https://zbmath.org/?q=an:0784.60095|0732.60116}
\transl
\jour J. Soviet Math.
\yr 1992
\vol 61
\issue 3
\pages 2114--2151
\crossref{https://doi.org/10.1007/BF01097527}
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