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Time-changed fractional Ornstein-Uhlenbeck process

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Universitá degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo I–80126, Napoli, Italy

    Giacomo Ascione

  2. Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska 64, Kyiv, 01601, Ukraine

    Yuliya Mishura

  3. Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Universitá degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo I–80126, Napoli, Italy

    Enrica Pirozzi

Authors
  1. Giacomo Ascione
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  2. Yuliya Mishura
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  3. Enrica Pirozzi
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Correspondence to Giacomo Ascione.

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Ascione, G., Mishura, Y. & Pirozzi, E. Time-changed fractional Ornstein-Uhlenbeck process. Fract Calc Appl Anal 23, 450–483 (2020). https://doi.org/10.1515/fca-2020-0022

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