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Title: A stochastic diffusion process for Lochner's generalized Dirichlet distribution

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:
 [1] ;  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-13-21573
Journal ID: ISSN 0022-2488; JMAPAQ
Grant/Contract Number:
AC52-06NA25396
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)
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Fokker-Planck equation, Stochastic diffusion, Generalized Dirichlet distribution
OSTI Identifier:
1233161

Bakosi, J., and Ristorcelli, J. R.. A stochastic diffusion process for Lochner's generalized Dirichlet distribution. United States: N. p., Web. doi:10.1063/1.4822416.
Bakosi, J., & Ristorcelli, J. R.. A stochastic diffusion process for Lochner's generalized Dirichlet distribution. United States. doi:10.1063/1.4822416.
Bakosi, J., and Ristorcelli, J. R.. 2013. "A stochastic diffusion process for Lochner's generalized Dirichlet distribution". United States. doi: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 = {2013},
month = {10}
}