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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ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 12–15, 2012
Chicago, Illinois, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-4502-8
PROCEEDINGS PAPER
Simulating Drift-Diffusion Processes With Generalized Interval Probability
Yan Wang
Yan Wang
Georgia Institute of Technology, Atlanta, GA
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Yan Wang
Georgia Institute of Technology, Atlanta, GA
Paper No:
DETC2012-70699, pp. 1201-1211; 11 pages
Published Online:
September 9, 2013
Citation
Wang, Y. "Simulating Drift-Diffusion Processes With Generalized Interval Probability." Proceedings of the ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 3: 38th Design Automation Conference, Parts A and B. Chicago, Illinois, USA. August 12–15, 2012. pp. 1201-1211. ASME. https://doi.org/10.1115/DETC2012-70699
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