Fokker-Planck-Kolmogorov equations associated with SDEs driven by time-changed fractional Brownian motion

Abstract

In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are suggested. The time-change process considered is either the first hitting time process for a stable subordinator or a mixture of stable subordinators. A family of operators arising in the representation of the Fokker-Plank-Kolmogorov equations is shown to have the semigroup property.

arXiv comment16 pages

Cited by in corpus (9)

• Generalized Elastic Model: Fractional Langevin Description, Fluctuation Relation, and Linear Response
• Time-Changed Poisson Processes
• Weak ergodicity breaking in an anomalous diffusion process of mixed origins
• On the fractional counterpart of the higher-order equations
• Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators
• Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift
• Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations
• Interacting Particle Systems in Time-Dependent Geometries
• Time-changed Dirac-Fokker-Planck equations on the lattice