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

Published online by Cambridge University Press:  21 September 2021

Giacomo Ascione
Affiliation:
Dipartimento di Matematica e Applicazioni ‘Renato Caccioppoli’, Universita degli Studi di Napoli Federico II, 80126 Napoli, Italy (giacomo.ascione@unina.it)
Yuliya Mishura
Affiliation:
Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, Kyiv 01601, Ukraine (myus@univ.kiev.ua)
Enrica Pirozzi
Affiliation:
Dipartimento di Matematica e Applicazioni ‘Renato Caccioppoli’, Universita degli Studi di Napoli Federico II, 80126 Napoli, Italy (enrica.pirozzi@unina.it)

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.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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