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Title: A Stochastic Diffusion Process for the Dirichlet Distribution

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N coupled 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 of N variables 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.
Authors:
 [1] ;  [1]
  1. Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Publication Date:
OSTI Identifier:
1198484
Type:
Published Article
Journal Name:
International Journal of Stochastic Analysis
Additional Journal Information:
Journal Volume: 2013; Related Information: CHORUS Timestamp: 2016-07-30 13:58:37; Journal ID: ISSN 2090-3332
Publisher:
Hindawi Publishing Corporation
Sponsoring Org:
USDOE
Country of Publication:
Egypt
Language:
English