scholarly journals Fundamental solution of fractional Kolmogorov–Fokker–Planck equation

2021 ◽  
Vol 1 ◽  
pp. 100031
Author(s):  
Cong He ◽  
Jingchun Chen ◽  
Houzhang Fang ◽  
Huan He
Keyword(s):  
Fundamental Solution ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals A STOCHASTIC DERIVATION OF THE GEODESIC RULE

2006 ◽  
Vol 21 (07) ◽  
pp. 1493-1502 ◽  
Author(s):  
NIKOS KALOGEROPOULOS
Keyword(s):  
Asymptotic Behavior ◽  
Random Walk ◽  
Fundamental Solution ◽  
Heat Kernel ◽  
Continuum Limit ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
The Continuum ◽  
Fokker Planck

We argue that the geodesic rule, for global defects, is a consequence of the randomness of the values of the Goldstone field ϕ in each causally connected volume. As these volumes collide and coalescence, ϕ evolves by performing a random walk on the vacuum manifold [Formula: see text]. We derive a Fokker–Planck equation that describes the continuum limit of this process. Its fundamental solution is the heat kernel on [Formula: see text], whose leading asymptotic behavior establishes the geodesic rule.

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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