Explicit formulas for the top Lyapunov exponents of planar linear stochastic differential equations

ABSTRACT

Our aim in this article is to establish explicit formulas for the top Lyapunov exponents of planar linear stochastic differential equations. We use these formulas to examine the sample-path stability of a linear stochastic differential equations arising in fluid dynamics and of a model of stochastic Hopf bifurcation.

KEYWORDS:

• Multiplicative ergodic theorem
• Lyapunov exponent
• stochastic differential equation
• stability, stochastic bifurcation

MATHEMATICS SUBJECT CLASSIFICATION:

• 37H15
• 37H10
• 37H20

Funding

The work of the second author is supported by the JSPS International Fellowship for Research in Japan (P15320).