# Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations

Fractional Calculus and Applied Analysis (2011)

- Volume: 14, Issue: 1, page 56-79
- ISSN: 1311-0454

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topHahn, Marjorie, and Umarov, Sabir. "Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations." Fractional Calculus and Applied Analysis 14.1 (2011): 56-79. <http://eudml.org/doc/219577>.

@article{Hahn2011,

abstract = {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.},

author = {Hahn, Marjorie, Umarov, Sabir},

journal = {Fractional Calculus and Applied Analysis},

keywords = {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},

language = {eng},

number = {1},

pages = {56-79},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations},

url = {http://eudml.org/doc/219577},

volume = {14},

year = {2011},

}

TY - JOUR

AU - Hahn, Marjorie

AU - Umarov, Sabir

TI - Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations

JO - Fractional Calculus and Applied Analysis

PY - 2011

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 14

IS - 1

SP - 56

EP - 79

AB - 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.

LA - eng

KW - 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

UR - http://eudml.org/doc/219577

ER -

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