Article ID Journal Published Year Pages File Type
561258 Mechanical Systems and Signal Processing 2013 13 Pages PDF
Abstract

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 differential Chapman–Kolmogorov equation based on a new generalized interval probability theory is derived, where epistemic uncertainty is modeled by the generalized interval while the aleatory one is by the probability measure. A generalized Fokker–Planck equation is proposed to describe drift-diffusion processes under both uncertainties. 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 method is demonstrated by numerical examples.

► Stochastic systems are described by a new generalized interval probability theory. ► A generalized differential Chapman–Kolmogorov equation is derived. ► A generalized Fokker–Planck equation is proposed for drift-diffusion processes. ► A path integral method is developed to model time evolution of interval probability. ► Interval-valued probability densities rigorously bound the real-valued solutions.

Related Topics
Physical Sciences and Engineering Computer Science Signal Processing
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