Random Time Dynamical Systems

TL;DR

This paper introduces random time changes in dynamical systems, analyzing how such modifications influence long-term behavior and decay rates, with implications for understanding complex stochastic dynamics.

Contribution

It presents a novel framework for incorporating random time changes into dynamical systems and studies their impact on asymptotic behavior and decay rates.

Findings

Random time changes slow down the decay of dynamical systems.

Subordination principles help analyze long-term behavior.

Random time characteristics influence the velocity of the dynamics.

Abstract

In this paper, we introduce the concept of random time changes in dynamical systems. The sub- ordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of random time, that the subordinated system exhibits a slower time decay which is determined by the random time characteristics. Along the path asymp- totic, a random time change is reflected in the new velocity of the resulting dynamics.