Cesaro Limits for Fractional Dynamics

TL;DR

This paper investigates the long-term behavior of dynamical systems altered by random time changes, focusing on Cesaro limits and their asymptotic properties, especially for stable subordinators and more general classes.

Contribution

It introduces three classes of random time changes and analyzes their asymptotic decay patterns, extending understanding beyond stable subordinators.

Findings

Explicit Cesaro limit expressions for stable subordinators

Asymptotic behavior characterized for various random time changes

Reduction of complex calculations to Cesaro limit analysis

Abstract

We study the asymptotic behavior of random time changes of dynamical systems. As random time changes we propose three classes which exhibits different patterns of asymptotic decays. The subordination principle may be applied to study the asymptotic behavior of the random time dynamical systems. It turns out that for the special case of stable subordinators explicit expressions for the subordination are known and its asymptotic behavior are derived. For more general classes of random time changes explicit calculations are essentially more complicated and we reduce our study to the asymptotic behavior of the corresponding Cesaro limit.