2019/06/05 by Solesne Bourguin, Bourguin, Solesne, Siragan Gailus +3 · 1 citation
Mathematics · Physics and Astronomy · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Advanced Thermodynamics and Statistical Mechanics #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1906.02131
This article studies typical dynamics and fluctuations for a slow-fast\ndynamical system perturbed by a small fractional Brownian noise. Based on an\nergodic theorem with explicit rates of convergence, which may be of independent\ninterest, we characterize the asymptotic dynamics of the slow component to two\norders (i.e., the typical dynamics and the fluctuations). The limiting\ndistribution of the fluctuations turns out to depend upon the manner in which\nthe small-noise parameter is taken to zero relative to the scale-separation\nparameter. We study also an extension of the original model in which the\nrelationship between the two small parameters leads to a qualitative difference\nin limiting behavior. The results of this paper provide an approximation, to\ntwo orders, to dynamical systems perturbed by small fractional Brownian noise\nand subject to multiscale effects.\n