Slow-fast systems with fractional environment and dynamics
Xue-Mei Li, Julian Sieber
Abstract
We prove a fractional averaging principle for interacting slow-fast systems. The mode of convergence is in Hölder norm in probability. The main technical result is a quenched ergodic theorem on the conditioned fractional dynamics. We also establish geometric ergodicity for a class of fractional-driven stochastic differential equations, improving a recent result of Panloup and Richard.
Topics & Concepts
MathematicsErgodicityErgodic theoryStochastic differential equationDynamical systems theoryConvergence (economics)Applied mathematicsFractional calculusNorm (philosophy)Fractional Brownian motionClass (philosophy)Pure mathematicsBrownian motionStatisticsArtificial intelligenceQuantum mechanicsEconomicsPhysicsComputer scienceLawEconomic growthPolitical scienceStochastic processes and statistical mechanicsStochastic processes and financial applicationsMathematical Dynamics and Fractals