On the low-dimensional modelling of Stratonovich stochastic differential equations

Chao Xu and A.J. Roberts

Physica A: Statistical Mechanics and its Applications, 1996, vol. 225, issue 1, 62-80

Abstract: We develop further ideas on how to construct low-dimensional models of stochastic dynamical systems. The aim is to derive a consistent and accurate model from the originally high-dimensional system. This is done with the support of centre manifold theory and techniques. Aspects of several previous approaches are combined and extended: adiabatic elimination has previously been used, but centre manifold techniques simplify the noise by removing memory effects, and with less algebraic effort than normal forms; analysis of associated Fokker-Plank equations replace nonlinearly generated noise processes by their long-term equivalent white noise. The ideas are developed by examining a simple dynamical system which serves as a prototype of more interesting physical situations.

Keywords: Stochastic differential equation; Centre manifold; Low-dimensional modelling; Noisy dynamical system; Fokker-Planck equation (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:225:y:1996:i:1:p:62-80

DOI: 10.1016/0378-4371(95)00387-8

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