# Random Time Change and Related Evolution Equations: Time Asymptotic Behavior

## TL;DR

This paper studies the long-term behavior of solutions to fractional evolution equations derived from random time changes in Markov processes, focusing on inverse subordinators and their asymptotic properties.

## Contribution

It introduces a framework for analyzing the asymptotic behavior of solutions to fractional evolution equations with inverse subordinators, expanding understanding of time asymptotics in stochastic processes.

## Key findings

- Characterization of subordinators suitable for asymptotic analysis
- Asymptotic behavior of solutions to fractional evolution equations
- Application of subordination principle to Kolmogorov equations

## Abstract

In this paper we investigate the long time behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We consider inverse subordinators as random times and use the subordination principle for the solutions to forward Kolmogorov equations. The class of subordinators for which asymptotic analysis may be realized is described.