2005/12/31 by Hideo Hasegawa
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1143/jpsj.75.033001
published as J. Phys. Soc. Jpn. 75 (2006) 033001 · 10 pages, 1 figure; accepted in J. Phys. Soc. Jpn. with minor changes
arxiv created 2006/01/13 · openalex publication_date 2006/03/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Finite N-unit Langevin models with additive and multiplicative noises have been studied with the use of the augmented moment method (AMM) previously proposed by the author [H. Hasegawa, Phys. Rev E \bf 67, 041903 (2003)]. Original N-dimensional stochastic equations are transformed to the three-dimensional deterministic equations for means and fluctuations of local and global variables. Calculated results of our AMM are in good agreement with those of direct simulations (DS). We have shown that although the effective strength of the additive noise of the N-unit system is scaled as β(N)=β(1)/√(N), it is not the case for multiplicative noise [α(N) ≠ α(1)/√(N)], where α(N) and β(N) denote the strength of multiplicative and additive noises, respectively, for the size-N system. It has been pointed out that the naive assumption of α(N) = α(1)/√(N) leads to result which violates the central-limit theorem and which does not agree with those of DS and AMM.