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A generalized Cauchy process having cubic nonlinearity. (English) Zbl 1235.62122

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:

62M09 Non-Markovian processes: estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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