Geodesic
Stability of infinite systems of stochastic equations
Itogi nauki i tehniki. Seriâ, Teoriâ veroâtnostej. Matematičeskaâ statistika. Teoretičeskaâ kibernetika, Itogi Nauki i Tekhniki. Seriya "Teoriya Veroyatnostei. Matematicheskaya Statistika. Teoreticheskaya Kibernetika", Tome 27 (1990), pp. 79-128 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{INTV_1990_27_a1,
     author = {I. A. Ignatyuk and V. A. Malyshev and T. S. Turova},
     title = {Stability of infinite systems of stochastic equations},
     journal = {Itogi nauki i tehniki. Seri\^a, Teori\^a vero\^atnostej. Matemati\v{c}eska\^a statistika. Teoreti\v{c}eska\^a kibernetika},
     pages = {79--128},
     year = {1990},
     volume = {27},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTV_1990_27_a1/}
}
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I. A. Ignatyuk; V. A. Malyshev; T. S. Turova. Stability of infinite systems of stochastic equations. Itogi nauki i tehniki. Seriâ, Teoriâ veroâtnostej. Matematičeskaâ statistika. Teoretičeskaâ kibernetika, Itogi Nauki i Tekhniki. Seriya "Teoriya Veroyatnostei. Matematicheskaya Statistika. Teoreticheskaya Kibernetika", Tome 27 (1990), pp. 79-128. http://geodesic.mathdoc.fr/item/INTV_1990_27_a1/