scholarly journals Fokker–Planck equation and path integral representation of the fractional Ornstein–Uhlenbeck process with two indices

2014 ◽  
Vol 47 (49) ◽  
pp. 495203
Author(s):  
Chai Hok Eab ◽  
S C Lim
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Planck Equation ◽  
Uhlenbeck Process ◽  
Path Integral Representation ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Two Indices ◽  
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.

The Fokker–Planck equation for the time-changed fractional Ornstein–Uhlenbeck stochastic process

2021 ◽  
pp. 1-26
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Mild Solutions ◽  
Sufficient Conditions ◽  
Planck Equation ◽  
Strong Solutions ◽  
Uniqueness Result ◽  
Uhlenbeck Process ◽  
Weak Maximum Principle ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

In this paper, we study some properties of the generalized Fokker–Planck equation induced by the time-changed fractional Ornstein–Uhlenbeck process. First of all, we exploit some sufficient conditions to show that a mild solution of such equation is actually a classical solution. Then, we discuss an isolation result for mild solutions. Finally, we prove the weak maximum principle for strong solutions of the aforementioned equation and then a uniqueness result.

Simulating Drift-Diffusion Processes With Generalized Interval Probability

2012 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Path Integral ◽  
Stochastic Systems ◽  
Diffusion Processes ◽  
Epistemic Uncertainty ◽  
Planck Equation ◽  
Integral Approach ◽  
Drift Diffusion ◽  
Interval Probability ◽  
Fokker Planck Equation ◽  
Fokker Planck

The Fokker-Planck equation is widely used to describe the time evolution of stochastic systems in drift-diffusion processes. Yet, it does not differentiate two types of uncertainties: aleatory uncertainty that is inherent randomness and epistemic uncertainty due to lack of perfect knowledge. In this paper, a generalized Fokker-Planck equation based on a new generalized interval probability theory is proposed to describe drift-diffusion processes under both uncertainties, where epistemic uncertainty is modeled by the generalized interval while the aleatory one is by the probability measure. A path integral approach is developed to numerically solve the generalized Fokker-Planck equation. The resulted interval-valued probability density functions rigorously bound the real-valued ones computed from the classical path integral method. The new approach is demonstrated by numerical examples.

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