scholarly journals Hitting time distributions for efficient simulations of drift‐diffusion processes

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Raghu Raghavan
Keyword(s):  
Diffusion Processes ◽  
Hitting Time ◽  
Drift Diffusion

Quantification of Model-Form Uncertainty in Drift-Diffusion Simulation Using Fractional Derivatives

2015 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Diffusion Processes ◽  
Planck Equation ◽  
Optimization Procedure ◽  
Physical World ◽  
Drift Diffusion ◽  
Long Range Correlations ◽  
Modeling Process ◽  
Model Form ◽  
Generic Description ◽  
Non Gaussian

In modeling and simulation, model-form uncertainty arises from the lack of knowledge and simplification during modeling process and numerical treatment for ease of computation. Traditional uncertainty quantification approaches are based on assumptions of stochasticity in real, reciprocal, or functional spaces to make them computationally tractable. This makes the prediction of important quantities of interest such as rare events difficult. In this paper, a new approach to capture model-form uncertainty is proposed. It is based on fractional calculus, and its flexibility allows us to model a family of non-Gaussian processes, which provides a more generic description of the physical world. A generalized fractional Fokker-Planck equation (fFPE) is proposed to describe the drift-diffusion processes under long-range correlations and memory effects. A new model calibration approach based on the maximum accumulative mutual information is also proposed to reduce model-form uncertainty, where an optimization procedure is taken.

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.

The Influence of Drift-Diffusion Processes onI–V Characteristics of Si Schottky Diodes

1993 ◽  
Vol 136 (2) ◽  
pp. 393-400
Author(s):  
S. S. Simeonov ◽  
E. I. Kafedjiiska ◽  
A. L. Guerassimov
Keyword(s):  
Diffusion Processes ◽  
Schottky Diodes ◽  
Drift Diffusion

scholarly journals On subclasses of infinitely divisible distributions on R related to hitting time distributions of 1-dimensional generalized diffusion processes

1992 ◽  
Vol 127 ◽  
pp. 175-200 ◽  
Author(s):  
Makoto Yamazato
Keyword(s):  
Laplace Transform ◽  
Diffusion Processes ◽  
Hitting Time ◽  
Infinitely Divisible Distributions ◽  
Strict Sense ◽  
Real Numbers ◽  
Positive Real ◽  
Infinitely Divisible

A distribution μ on R+ = [0, ∞) is said to be a distribution if there are an increasing (in the strict sense) sequence of positive real numbers such that, for each j = 0, …, m, there is at least one ak satisfying bj < ak < b+1 and theLaplace transform of μ is represented as

scholarly journals Hitting time distributions of single points for 1-dimensional generalized diffusion processes

1990 ◽  
Vol 119 ◽  
pp. 143-172 ◽  
Author(s):  
Makoto Yamazato
Keyword(s):  
Diffusion Processes ◽  
Hitting Time ◽  
One Dimensional

In this paper, we will characterize the class of (conditional) hitting time distributions of single points of one dimensional generalized diffusion processes and give their tail behaviors in terms of speed measures of the generalized diffusion processes.

Passage time moments for multidimensional diffusions

2000 ◽  
Vol 37 (1) ◽  
pp. 246-251 ◽  
Author(s):  
S. Balaji ◽  
S. Ramasubramanian
Keyword(s):  
Brownian Motion ◽  
Diffusion Process ◽  
Diffusion Processes ◽  
Passage Time ◽  
Hitting Time ◽  
Two Dimensional ◽  
Reflecting Brownian Motion ◽  
Multidimensional Diffusions ◽  
Multidimensional Diffusion

Let τr denote the hitting time of B(0:r) for a multidimensional diffusion process. We give verifiable criteria for finiteness/infiniteness of As an application we exhibit classes of diffusion processes which are recurrent but is infinite for all p > 0, |x| > r > 0; this includes the two-dimensional Brownian motion and the reflecting Brownian motion in a wedge with a certain parameter α = 0.

Model-Form Calibration in Drift-Diffusion Simulation Using Fractional Derivatives

2016 ◽  
Vol 2 (3) ◽  
Author(s):  
Yan Wang
Keyword(s):  
Diffusion Processes ◽  
Planck Equation ◽  
Optimization Procedure ◽  
Physical World ◽  
Drift Diffusion ◽  
Long Range Correlations ◽  
Model Form ◽  
Maximum Mutual Information ◽  
Generic Description ◽  
Non Gaussian

In modeling and simulation, model-form uncertainty arises from the lack of knowledge and simplification during the modeling process and numerical treatment for ease of computation. Traditional uncertainty quantification (UQ) approaches are based on assumptions of stochasticity in real, reciprocal, or functional spaces to make them computationally tractable. This makes the prediction of important quantities of interest, such as rare events, difficult. In this paper, a new approach to capture model-form uncertainty is proposed. It is based on fractional calculus, and its flexibility allows us to model a family of non-Gaussian processes, which provides a more generic description of the physical world. A generalized fractional Fokker–Planck equation (fFPE) is used to describe the drift-diffusion processes under long-range correlations and memory effects. A new model-calibration approach based on the maximum mutual information is proposed to reduce model-form uncertainty, where an optimization procedure is taken.

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