On the linearization of nonlinear Langevin-type stochastic differential equations. (English) Zbl 0587.60047

We show that a logical extension of the piecewise optimal linearization procedure leads to the Gaussian decoupling scheme, where no iteration is required. The scheme is equivalent to solving a few coupled equations. The method is applied to models which represent (a) a single steady state, (b) passage from an initial unstable state to a final preferred stable state by virtue of a finite displacement from the unstable state, and (c) a bivariate case of passage from an unstable state to a final stable state.
The results are shown to be in very good agreement with the Monte Carlo calculations carried out for these cases. The method should be of much value in multidimensional cases.


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65C05 Monte Carlo methods
81P20 Stochastic mechanics (including stochastic electrodynamics)
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[1] R. F. Fox,Phys. Rep. 48:179 (1978).
[2] N. G. Van Kampen,Phys. Rep. 24:171 (1976).
[3] A. Budgor,J. Stat. Phys. 15:355 (1976).
[4] A. Budgor, K. Lindenberg, and K. E. Shuler,J. Stat. Phys. 15:375 (1976).
[5] B. J. West, K. Lindenberg, and K. E. Shuler,J. Stat. Phys. 18:217 (1978).
[6] A. Budgor and B. J. West,Phys. Rev. A 17:370 (1978).
[7] J. O. Eaves and W. P. Reinhardt,J. Stat. Phys. 25:127 (1981); and references therein.
[8] M. Suzuki, inAdvances in Chemical Physics, Vol. 46, I. Prigogine and S. Rice, eds. (John Wiley and Sons, New York, 1981).
[9] M. Suzuki, inProceedings on the XVIIth Salvay Conference on Physics, G. Nicolis, G. Dewel, and J. W. Turner, eds. (John Wiley and Sons, New York, 1981).
[10] G. Ananthakrishna,J. Phys. D 15:77 (1982).
[11] G. Ananthakrishna, M. C. Valsakumar, and K. P. N. Murthy, to be published.
[12] M. Suzuki and S. Miyashita, to be published (see Ref. 8).
[13] J. S. Langer, M. Bar-on, and H. D. Miller,Phys. Rev. A 11:1417 (1975).
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