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arXiv · 1811.10417

A fractional generalized Cauchy process

Yusuke Uchiyama·Takanori Kadoya·Hidetoshi Konno
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Abstract

This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics during random time durations, whose analytical representation is given by the It$\hat{\rm o}$ stochastic integral. The associated probability density function is given by the Tsallis $q$-Gaussian distribution at the stationary state. The method of fractional Feynman-Kac formula shows that weak ergodicity breaking of the FGCP depends on the existence of the subordinator and/or the divergence of variance.

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BibTeXRIS

Yusuke Uchiyama, Takanori Kadoya, Hidetoshi Konno. 2018-11-22. A fractional generalized Cauchy process. https://doi.org/10.1103/physreve.99.032119

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