A stochastic diffusion process for Lochner's generalized Dirichlet distribution
Abstract
The method of potential solutions of FokkerPlanck 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 FokkerPlanck equation developed here, satisfy a unitsum 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 Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1233161
 Report Number(s):
 LAUR1321573
Journal ID: ISSN 00222488; JMAPAQ
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Mathematical Physics
 Additional Journal Information:
 Journal Volume: 54; Journal Issue: 10; Journal ID: ISSN 00222488
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; FokkerPlanck 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 FokkerPlanck 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 FokkerPlanck equation developed here, satisfy a unitsum 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}
}
Web of Science