Explicit expressions for the Lyapunov exponents of certain Markov processes
نویسندگان
چکیده
A method for the explicit computation of the Lyapunov exponents of certain Markov processes is developed. Its utility is demonstrated by an application to two-dimensional random evolution differential equations. Our approach exploits the relation between the Lyapunov exponent and the p-moment Lyapunov exponents, as was first observed and studied by Arnold [1]. The p-moment Lyapunov exponent is characterized by the domain in which the Laplace transform of t -*E|x(t)| is finite. We apply our results to the random harmonic oscillator and derive an explicit expression for the Lyapunov exponent. In a simple case it is computed by quadratures. Key words-* Lyapunov exponents, p-moment Lyapunov exponents, random evolution differential equations, random harmonic oscillator. AMS(MOS) subject classification: Primary 93E15, 34F05; Secondary 60J25, 70L05. Explicit expressions for the Lyapunov exponents of certain stochastic processes
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