Date of Completion

8-30-2013

Embargo Period

8-30-2013

Major Advisor

Maria Gordina

Associate Advisor

Alexander Teplyaev

Associate Advisor

Richard Bass

Field of Study

Mathematics

Open Access

Open Access

Abstract

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.

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