Lyapunov exponents of nilpotent ito systems
- 1 September 1988
- journal article
- research article
- Published by Taylor & Francis in Stochastics
- Vol. 25 (1) , 43-57
- https://doi.org/10.1080/17442508808833531
Abstract
In all previous work on Lyapunov exponents for stochastic systems, the results take the form of asymptotic power series expansions in the noise parameter. In this paper we consider a natural class of systems driven by white noise for which the asymptotic expansions contain fractional powers of the noise parameter. In particular we obtain an exact formula for certain cases. The systems studied include the free particle with multiplicative white noise and mechanical systems with one degree of freedom. The results are stated and proved for small noise and large noiseKeywords
This publication has 6 references indexed in Scilit:
- Lyapunov Exponent and Rotation Number of Two-Dimensional Linear Stochastic Systems with Small DiffusionSIAM Journal on Applied Mathematics, 1988
- Asymptotic Analysis of the Lyapunov Exponent and Rotation Number of the Random Oscillator and ApplicationsSIAM Journal on Applied Mathematics, 1986
- Almost sure and moment stability for linear ito equationsLecture Notes in Mathematics, 1986
- Asymptotic expansions of the Liapunov index for linear stochastic systems with small noiseJournal of Applied Mathematics and Mechanics, 1982
- A classification of the second order degenerate elliptic operators and its probabilistic characterizationProbability Theory and Related Fields, 1974
- Controllability of nonlinear systemsJournal of Differential Equations, 1972