A stochastic diffusion process for Lochner's generalized Dirichlet distribution
Abstract
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner’s generalized Dirichlet distribution as its asymptotic solution. Individual samples of a discrete ensemble, obtained from the system of stochastic differential equations, equivalent to the Fokker-Planck equation developed here, satisfy a unit-sum constraint at all times and ensure a bounded sample space, similarly to the process developed in for the Dirichlet distribution. Consequently, the generalized Dirichlet diffusion process may be used to represent realizations of a fluctuating ensemble of N variables subject to a conservation principle. Compared to the Dirichlet distribution and process, the additional parameters of the generalized Dirichlet distribution allow a more general class of physical processes to be modeled with a more general covariance matrix.
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1233161
- Report Number(s):
- LA-UR-13-21573
Journal ID: ISSN 0022-2488; JMAPAQ
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Mathematical Physics
- Additional Journal Information:
- Journal Volume: 54; Journal Issue: 10; Journal ID: ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Fokker-Planck equation, Stochastic diffusion, Generalized Dirichlet distribution
Citation Formats
Bakosi, J., and Ristorcelli, J. R. A stochastic diffusion process for Lochner's generalized Dirichlet distribution. United States: N. p., 2013.
Web. doi:10.1063/1.4822416.
Bakosi, J., & Ristorcelli, J. R. A stochastic diffusion process for Lochner's generalized Dirichlet distribution. United States. https://doi.org/10.1063/1.4822416
Bakosi, J., and Ristorcelli, J. R. Tue .
"A stochastic diffusion process for Lochner's generalized Dirichlet distribution". United States. https://doi.org/10.1063/1.4822416. https://www.osti.gov/servlets/purl/1233161.
@article{osti_1233161,
title = {A stochastic diffusion process for Lochner's generalized Dirichlet distribution},
author = {Bakosi, J. and Ristorcelli, J. R.},
abstractNote = {The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner’s generalized Dirichlet distribution as its asymptotic solution. Individual samples of a discrete ensemble, obtained from the system of stochastic differential equations, equivalent to the Fokker-Planck equation developed here, satisfy a unit-sum constraint at all times and ensure a bounded sample space, similarly to the process developed in for the Dirichlet distribution. Consequently, the generalized Dirichlet diffusion process may be used to represent realizations of a fluctuating ensemble of N variables subject to a conservation principle. Compared to the Dirichlet distribution and process, the additional parameters of the generalized Dirichlet distribution allow a more general class of physical processes to be modeled with a more general covariance matrix.},
doi = {10.1063/1.4822416},
journal = {Journal of Mathematical Physics},
number = 10,
volume = 54,
place = {United States},
year = {Tue Oct 01 00:00:00 EDT 2013},
month = {Tue Oct 01 00:00:00 EDT 2013}
}
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Works referencing / citing this record:
Diffusion Processes Satisfying a Conservation Law Constraint
journal, March 2014
- Bakosi, J.; Ristorcelli, J. R.
- International Journal of Stochastic Analysis, Vol. 2014