A0681
Title: Statistical view of chaos and its detection
Authors: Yan Liu - Waseda University (Japan) [presenting]
Rintaro Ichiya - Waseda University (Japan)
Rinka Sagawa - Waseda University (Japan)
Abstract: The chaos is discussed from a statistical viewpoint. For deterministic dynamical systems, the chaotic behaviors are detected by the Lyapunov exponents. A macroscopic hypothesis is introduced for the chaotic behaviors in nonlinear stochastic processes based on the population of Lyapunov exponents. To be specific, the local block Lyapunov exponent and the diagonal Lyapunov dispersion ratio are introduced as fundamental statistical tools to distinguish chaotic behaviors. The asymptotic theories are developed for these statistical tools under a general setting. Numerical simulations under different parameter settings illustrate the satisfactory performance of the statistical approach. This method is also applied to the financial market data, providing evidence for the possible chaotic behaviors in the data.
