A Stochastic Diffusion Process for the Dirichlet Distribution
- Los Alamos National Laboratory, Los Alamos, NM 87545, USA
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability ofNcoupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded sample space, a coupled nonlinear diffusion process is required: the Wiener processes in the equivalent system of stochastic differential equations are multiplicative with coefficients dependent on all the stochastic variables. Individual samples of a discrete ensemble, obtained from the stochastic process, satisfy a unit-sum constraint at all times. The process may be used to represent realizations of a fluctuating ensemble ofNvariables subject to a conservation principle. Similar to the multivariate Wright-Fisher process, whose invariant is also Dirichlet, the univariate case yields a process whose invariant is the beta distribution. As a test of the results, Monte Carlo simulations are used to evolve numerical ensembles toward the invariant Dirichlet distribution.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1198484
- Alternate ID(s):
- OSTI ID: 1233159
- Report Number(s):
- LA-UR-12-26980; PII: 842981; 842981
- Journal Information:
- International Journal of Stochastic Analysis, Journal Name: International Journal of Stochastic Analysis Vol. 2013; ISSN 2090-3332
- Publisher:
- Hindawi Publishing CorporationCopyright Statement
- Country of Publication:
- Egypt
- Language:
- English
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