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

Hahn, 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 -