Noise-intensity fluctuation in Langevin model and its higher-order Fokker–Planck equation

Yoshihiko Hasegawa and Masanori Arita

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 6, 1051-1063

Abstract: In this paper, we investigate a Langevin model subjected to stochastic intensity noise (SIN), which incorporates temporal fluctuations in noise-intensity. We derive a higher-order Fokker–Planck equation (HFPE) of the system, taking into account the effect of SIN by the adiabatic elimination technique. Stationary distributions of the HFPE are calculated by using the perturbation expansion. We investigate the effect of SIN in three cases: (a) parabolic and quartic bistable potentials with additive noise, (b) a quartic potential with multiplicative noise, and (c) a stochastic gene expression model. We find that the existence of noise-intensity fluctuations induces an intriguing phenomenon of a bimodal-to-trimodal transition in probability distributions. These results are validated with Monte Carlo simulations.

Keywords: Stochastic process; Superstatistics; Stochastic volatility; Adiabatic elimination; Higher-order Fokker–Planck equation (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:6:p:1051-1063

DOI: 10.1016/j.physa.2010.11.007

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