A fractional generalized Cauchy process

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$\hat{\mathrm{o}}$ 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.