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A Stochastic Diffusion Process for the Dirichlet Distribution

Journal Article · · International Journal of Stochastic Analysis
DOI:https://doi.org/10.1155/2013/842981· OSTI ID:1198484
 [1];  [1]
  1. Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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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.

Sponsoring Organization:
USDOE
OSTI ID:
1198484
Alternate ID(s):
OSTI ID: 1233159
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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