Time-changed fractional Ornstein-Uhlenbeck process

Abstract

We define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

27 pages

References in corpus (3)

• Fractional Cox--Ingersoll--Ross process with non-zero <<mean>>
• Correlation structure of time-changed fractional Brownian motion
• Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations

Cited by in corpus (4)

• Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations
• Stochastic solutions of generalized time-fractional evolution equations
• The Fokker-Planck equation for the time-changed fractional Ornstein-Uhlenbeck process
• Asymptotic behaviour and functional limit theorems for a time changed Wiener process