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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Marjorie G. Hahn, Kei Kobayashi and Sabir Umarov
Journal: Proc. Amer. Math. Soc. 139 (2011), 691-705
MSC (2010): Primary 60G22, 35Q84
Published electronically: August 5, 2010
MathSciNet review: 2736349
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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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Additional Information

Marjorie G. Hahn
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Email: marjorie.hahn@tufts.edu

Kei Kobayashi
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Email: kei.kobayashi@tufts.edu

Sabir Umarov
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Email: sabir.umarov@tufts.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10527-0
PII: S 0002-9939(2010)10527-0
Keywords: Fractional Brownian motion, Fokker-Plank-Kolmogorov equation, governing equation, stable subordinator, time change
Received by editor(s): February 14, 2010
Received by editor(s) in revised form: March 19, 2010, and April 5, 2010
Published electronically: August 5, 2010
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.