2015/03/23 by Michele Bonnin, Bonnin, Michele
Physics and Astronomy · #FOS: Physical sciences #Scientific Research and Discoveries #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1503.06603
openalex publication_date 2015/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A description in terms of phase and amplitude variables is given, for nonlinear oscillators subject to white Gaussian noise described by Itô stochastic differential equations. The stochastic differential equations derived for the amplitude and the phase are rigorous, and their validity is not limited to the weak noise limit. If the noise intensity is small, the equations can be efficiently solved using asymptotic expansions. Formulas for the expected angular frequency, expected oscillation amplitude and amplitude variance are derived using Itô calculus.