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.

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

Ascione G.;Mishura Y.;Pirozzi E.
2021

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/868564
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