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Zbl 1235.62122
Konno, Hidetoshi; Tamura, Yoshiyasu
A generalized Cauchy process having cubic nonlinearity. (English)
[J] Rep. Math. Phys. 67, No. 2, 179-195 (2011). ISSN 0034-4877

Summary: A generalized Cauchy process with a cubic nonlinear term (a nonlinear friction) is studied under the influence of independent multiplicative and additive Gaussian-white noise. Three methods of parameter estimation (i.e., maximum likelihood, moment and log-amplitude moment) are presented in detail. The effect of nonlinearity-noise mterplay associated with the nonlinear friction under the influences of both multiplicative and additive noises are discussed in conjunction with fluctuation-dissipation theorem. The physical significance of nonlinear friction is demonstrated with the use of time series data in economics and fluid turbulence.

MSC 2000:: *62M09 Non-Markovian processes: estimation
62M10 Time series, etc. (statistics)

Keywords: methods of parameter estimation; nonlinearity-noise mterplay; physical signfficance

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Zentralblatt MATH Berlin [Germany]