Lyapunov exponents of nilpotent Itô systems. (English) Zbl 0654.60043

Pinsky, M. A.; Wihstutz, Volker

Stochastics 25, No. 1, 43-57 (1988).

Summary: In all previous work on Lyapunov exponents for stochastic systems, the results take the form of asymptotic power series expansion 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 noise.

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

hypoellipticity; random Schrödinger equation; Lyapunov exponents; power series expansion

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