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Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations

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Abstract

There is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called Fokker-Planck equations, also called Kolmogorov equations. The Brownian motion plays the role of the basic driving process for SDEs. This paper provides fractional generalizations of the triple relationship between the driving process, corresponding SDEs and deterministic fractional order Fokker-Planck-Kolmogorov type equations.

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Authors and Affiliations

  1. Department of Mathematics, Tufts University, Medford, MA, 02155, USA

    Marjorie Hahn & Sabir Umarov

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  1. Marjorie Hahn
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  2. Sabir Umarov
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Correspondence to Marjorie Hahn.

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Dedicated to 80-th anniversary of Professor Rudolf Gorenflo

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Hahn, M., Umarov, S. Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations. fcaa 14, 56–79 (2011). https://doi.org/10.2478/s13540-011-0005-9

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