Computing Lyapunov constants for random recurrences with smooth coefficients

Wright, Thomas G. and Trefethen, Lloyd N. (2000) Computing Lyapunov constants for random recurrences with smooth coefficients. Technical Report. Unspecified. (Submitted)

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Abstract

In recent years, there has been much interest in the growth and decay rates (Lyapunov constants) of solutions to random recurrences such as the random Fibonacci sequence . Many of these problems involve non-smooth dynamics (nondifferentiable invariant measures), making computations hard. Here, however, we consider recurrences with smooth random coefficients and smooth invariant measures. By computing discretised invariant measures and applying Richardson extrapolation, we can compute Lyapunov constants to ten digits of accuracy. In particular, solutions to the recurrence , where the are independent standard normal variables, increase exponentially (almost surely) at the asymptotic rate . Solutions to the related recurrences , and (where the are also independent standard normal variables) increase (decrease) at the rates and respectively.

Item Type: Technical Report (Technical Report) H - N > Numerical analysis Numerical Analysis Group 1280 Lotti Ekert 01 Jun 2011 09:20 01 Jun 2011 09:20

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