A stochastic diffusion process for Lochner's generalized Dirichlet distribution
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1233161
- Report Number(s):
- LA-UR-13-21573; JMAPAQ
- Journal Information:
- Journal of Mathematical Physics, Vol. 54, Issue 10; ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Diffusion Processes Satisfying a Conservation Law Constraint
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journal | March 2014 |
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