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

Hahn, Marjorie; Kobayashi, Kei; Umarov, Sabir

doi:10.1090/S0002-9939-2010-10527-0

Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion
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by Marjorie G. Hahn, Kei Kobayashi and Sabir Umarov PDF

Proc. Amer. Math. Soc. 139 (2011), 691-705 Request permission

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 the first hitting time process for either 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.

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