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APS » Journals » Phys. Rev. Lett. » Volume 79 » Issue 6
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Phys. Rev. Lett. 79, 966–969 (1997)

Stable Infinite Variance Fluctuations in Randomly Amplified Langevin Systems

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Hideki Takayasu
Sony Computer Science Laboratory, Takanawa Muse Building, 3-14-13 Higashi-Gotanda, Shinagawa-ku, Tokyo 151, Japan

Aki-Hiro Sato
Graduate School of Information Sciences, Tohoku University, Sendai 980-77, Japan

Misako Takayasu
“Research for the Future” Project, Faculty of Sciences and Technology, Keio University, Shin-Kawasaki-Mitsui Building West 3F, 890-12 Kashimada Saiwai-ku, Kawasaki-shi, Japan, 221

Received 26 December 1996; revised 21 March 1997; published in the issue dated 11 August 1997

A general discrete stochastic process involving random amplification with additive external noise is analyzed theoretically and numerically. Necessary and sufficient conditions to realize steady power law fluctuations with divergent variance are clarified. The power law exponent is determined by a statistical property of amplification independent of the external noise. By introducing a nonlinear effect a stretched exponential decay appears in the power law.

© 1997 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.79.966
DOI:
10.1103/PhysRevLett.79.966
PACS:
05.40.+j, 02.50.-r, 05.70.Ln, 64.60.Lx
 
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