2003/01/15 by Kirone Mallick, Philippe Marcq · 2 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Quantum chaos and dynamical systems #Stochastic processes and financial applications #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/s0378-4371(03)00200-0
published as Physica A Vol. 325, pp. 213-219 (2003) · To be published in Physica A
arxiv created 2003/01/15 · openalex publication_date 2003/04/23 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow algebraically with time before the dissipative time scale is reached, and calculate the associated anomalous diffusion exponents. In the case of colored noise, with a nonzero but arbitrarily small correlation time, the characteristic exponents are modified. We determine their values thanks to a self-consistent Ansatz.