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2011•Electronic Communications in ProbabilityOpen access

On time-changed Gaussian processes and their associated Fokker-Planck-Kolmogorov equations

Marjorie G. Hahn, Jelena Ryvkina, Kei Kobayashi, Sabir R. Umarov

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Abstract

This paper establishes Fokker-Planck-Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed Ornstein-Uhlenbeck process. The time-change process considered is the inverse of either a stable subordinator or a mixture of independent stable subordinators.

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What this paper is about

This paper establishes Fokker-Planck-Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed Ornstein-Uhlenbeck process. The time-change process considered is the inverse of either a stable subordinator or a mixture of independent stable subordinators.

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Available abstract

This paper establishes Fokker-Planck-Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed Ornstein-Uhlenbeck process. The time-change process considered is the inverse of either a stable subordinator or a mixture of independent stable subordinators.

Key concepts: Subordinator, Fokker–Planck equation, Mathematics, Fractional Brownian motion, Statistical physics, Kolmogorov equations (Markov jump process), Inverse Gaussian distribution, Gaussian process

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