Asymptotics for time-changed diffusions

TL;DR

This paper studies the long-term behavior of diffusions altered by time changes, especially focusing on generators with discontinuous coefficients and their associated PDEs.

Contribution

It provides new asymptotic analysis results for time-changed diffusions with discontinuous generator coefficients.

Findings

Asymptotic behaviors depend on coefficient discontinuities

Connections between PDEs and time-changed diffusions are clarified

Results inform the stability and long-term properties of such processes

Abstract

We consider time-changed diffusions driven by generators with discontinuous coefficients. The PDE's connections are investigated and in particular some results on the asymptotic analysis according to the behaviour of the coefficients are presented.