Large noise asymptotics of invariant measures, with applications to lyapunov exponents

We prove a basically necessary and sufficient criterion under which is stabilizable by parametric white noise which is only permitted to be applied to a prescribed set of entries of A. Mathematically, this leads to a non-classical averaging problem in which the large noise is degenerate (not hypo-el...

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Veröffentlicht in:	Stochastics and stochastics reports 1996-10, Vol.59 (1-2), p.71-142
Hauptverfasser:	Arnold, Ludwig, Eizenberg, Alex, Wihstutzc, Volker
Format:	Artikel
Sprache:	eng
Schlagworte:	1991 Mathematics Subject Classsification averaging large deviations Exact sciences and technology large noise asymptotics of invariant measures Lyapunov exponents Mathematical analysis Mathematics Measure and integration Operator theory Primary: 93E15 Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Secondary: 34D08 34F05 60H10 Sequences, series, summability stabilization by noise Stochastic processes
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Beschreibung
Zusammenfassung:	We prove a basically necessary and sufficient criterion under which is stabilizable by parametric white noise which is only permitted to be applied to a prescribed set of entries of A. Mathematically, this leads to a non-classical averaging problem in which the large noise is degenerate (not hypo-elliptic), and the averaged system has many invariant measures. Delicate estimates are necessary to prove "non-uniqueness breaking" of the sequence of invariant measures
ISSN:	1045-1129 1029-0346
DOI:	10.1080/17442509608834085