The Fokker-Planck equation for the time-changed fractional Ornstein-Uhlenbeck process

TL;DR

This paper investigates the properties of the generalized Fokker-Planck equation associated with the time-changed fractional Ornstein-Uhlenbeck process, establishing conditions for solutions and their uniqueness.

Contribution

It provides new conditions under which mild solutions are classical, discusses solution isolation, and proves maximum principles and uniqueness for the equation.

Findings

Mild solutions can be classical under certain conditions

Isolation results for solutions are established

Weak maximum principle and uniqueness are proved

Abstract

In this paper we study some properties of the generalized Fokker-Planck equation induced by the time-changed fractional Ornstein-Uhlenbeck process. First of all, we exploit some sufficient conditions to show that a mild solution of such equation is actually a classical solution. Then we discuss an isolation result for mild solutions. Finally, we prove the weak maximum principle for strong solutions of the aforementioned equation and then a uniqueness result.