2011/10/31 by T. Srokowski, Tomasz Srokowski · 20 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Acoustics #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Complex Systems and Time Series Analysis #Computer science #Diffusion #Distribution (mathematics) #Gradient noise #Inertia #Interpretation (philosophy) #Mathematical analysis #Mathematics #Multiplicative noise #Noise (video) #Noise floor #Noise measurement #Noise reduction #Physics #Quantum mechanics #Relaxation (psychology) #Statistical physics #Statistics #Value noise #White noise #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.85.021118
published in Physical Review E 85(2), 021118 (American Physical Society) · 11 pages, 6 figures
openalex publication_date 2012/02/13 · arxiv created 2012/02/14 · arxiv updated 2012/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Dynamical systems driven by a general Lévy stable noise are considered. The inertia is included and the noise, represented by a generalized Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive noise) is solved: the resulting distribution converges with time to the distribution for the white-noise, massless case. Moreover, a multiplicative noise is discussed. It can make the distribution steeper and the variance, which is finite, depends sublinearly on time (subdiffusion). For a small mass, a white-noise limit corresponds to the Stratonovich interpretation. On the other hand, the distribution tails agree with the Itô interpretation if the inertia is very large. An escape time from the potential well is calculated.