Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations
Fractional Calculus and Applied Analysis, Tome 14 (2011) no. 1, p. 56.

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MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf GorenfloThere 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.
Classification : 35R11, 35R60, 82C31, 60H10, 35Q84, 35-02
Mots-clés : Fractional Differential Equation (FDE), Lévy Process, Time-Change, Stable Subordinator, Stochastic Differential Equation (SDE), Fokker-Planck Equation, Kolmogorov Equations, fractional differential equations (FDE), Lévy process, stable subordinator, stochastic differential equations (SDE), Fokker-Planck equation, Kolmogorov equations 
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     author = {Hahn, Marjorie and Umarov, Sabir},
     title = {Fractional {Fokker-Planck-Kolmogorov} type {Equations} and their {Associated} {Stochastic} {Differential} {Equations}},
     journal = {Fractional Calculus and Applied Analysis},
     pages = {56},
     publisher = {mathdoc},
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     year = {2011},
     zbl = {1273.35293},
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Hahn, Marjorie; Umarov, Sabir. Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations. Fractional Calculus and Applied Analysis, Tome 14 (2011) no. 1, p. 56. https://geodesic-test.mathdoc.fr/item/FCAA_2011__14_1_219577/