Prog. Theor. Phys. Vol. 68 No. 1 (1982) pp. 98-115

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Critical Slowing Down in Stochastic Precesses. II

— Noise-Induced Long-Time Tail in Random Growing-Rate Models —

Masuo Suzuki, Shinji Takesue and Fumiyoshi Sasagawa

Department of Physics, University of Tokyo, Tokyo 113

(Received February 15, 1982)

Abstract:

Exact solutions of the random growing-rate models dx/dt = (γ+ η(t))x- gx^m for Gaussian white noise η(t) are obtained for an arbitrary value of m(>1) to give the noise-induced long-time tail <x^p(t)>≃t^-1/2 for large t at the critical point for any positive value of p. This confirms the phenomenological arguments in the first paper of this series. That is, this noise-induced long-time tail appears due to the balance (or cancellation) between the nonlinear term and noise term. Another intuitive explanation of this noise-induced long-time tail is presented on the basis of the asymptotic behavior of the normalization factor for the distribution function. A slowing down of <x^p(t)> for p<0 at a `transition point' γ=γ(p) = |p| ε is also discussed.

URL : http://ptp.ipap.jp/link?PTP/68/98/
DOI : 10.1143/PTP.68.98

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Citing Article(s) :

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Progress of Theoretical Physics Vol. 70 No. 1 (1983) pp. 312-314 :
Relaxation of Systems under the Effect of a Gaussian White Noise

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Progress of Theoretical Physics Vol. 72 No. 6 (1984) pp. 1255-1257 :
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Progress of Theoretical Physics Vol. 74 No. 5 (1985) pp. 1013-1021 :
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