scholarly journals Controllability to equilibria of the 1-D fokker-planck equation with zero-flux boundary condition

2017 ◽  
Author(s):  
Karthik Elamvazhuthi ◽  
Hendrik Kuiper ◽  
Spring Berman
Keyword(s):  
Boundary Condition ◽  
Planck Equation ◽  
Flux Boundary Condition ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Fractional Fokker-Planck-Kolmogorov equations associated with SDES on a bounded domain

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Sabir Umarov
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Stochastic Differential Equation ◽  
Bounded Domain ◽  
Planck Equation ◽  
Initial Boundary ◽  
Order Differential Operator ◽  
Fokker Planck Equation ◽  
Initial Boundary Value ◽  
Fokker Planck

AbstractThis paper is devoted to the fractional generalization of the Fokker-Planck equation associated with a nonlinear stochastic differential equation on a bounded domain. The driving process of the stochastic differential equation is a Lévy process subordinated to the inverse of Lévy’s mixed stable subordinators. The Fokker-Planck equation is given through the general Waldenfels operator, while the boundary condition is given through the general Wentcel’s boundary condition. As a fractional operator a distributed order differential operator with a Borel mixing measure is considered. In the paper fractional generalizations of the Fokker-Planck equation are derived and the existence of a unique solution of the corresponding initial-boundary value problems is proved.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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