Title: Detection of chaotic behaviors in stochastic systems by dispersion ratios in local block Lyapunov exponents diagrams Authors:  Yan Liu - Waseda University (Japan) [presenting]
Rintaro Ichiya - Waseda University (Japan)
Rinka Sagawa - Waseda University (Japan)
Abstract: Statistical methods are presented for quantifying chaotic behaviors in stochastic processes. We introduce the local block Lyapunov exponent and the diagonal Lyapunov dispersion ratio as fundamental statistical tools to distinguish chaotic behaviors in stochastic processes. We develop the asymptotic theories for these statistical tools under a general setting. As a macroscopic measure, we quantify the sensitive dependence induced by chaos in each block, and investigate the distributional distortion in stochastic processes. Numerical simulations under different parameter settings illustrate the satisfactory performance of our statistical approach. We also apply this method to the financial market data, providing evidence for the possible chaotic behaviors in the data.