The Top Lyapunov Exponent of Symplectic Stochastic Differential Equations: Theory and Numerics
Date of Completion
Field of Study
We calculate the top Lyapunov exponent for solutions to linear stochastic differ- ential equations with non-commuting drift and diffusion matrices. In particular we consider (1) a class of Rd-valued stochastic differential equations arising in the study of the noisy harmonic oscillator (2) Sp(2, R)-valued stochastic differential equations are considered. Additionally, numerical bounds are provided and simulation techniques are discussed with an example.
Baldenko, Alex, "The Top Lyapunov Exponent of Symplectic Stochastic Differential Equations: Theory and Numerics" (2013). Doctoral Dissertations. 240.