A stochastic diffusion process for Lochner's generalized Dirichlet distribution

Bakosi, J.; Ristorcelli, J. R.

doi:10.1063/1.4822416

A stochastic diffusion process for Lochner's generalized Dirichlet distribution

Journal Article · Tue Oct 01 00:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4822416· OSTI ID:1233161

Bakosi, J. ^[1]; Ristorcelli, J. R. ^[1]

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.

View Accepted Manuscript (DOE)

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

Journal Information:: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 54; ISSN JMAPAQ; ISSN 0022-2488

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (16)

Numerical Correlation and Petrographic Variation Chayes, F. The Journal of Geology, Vol. 70, Issue 4 https://doi.org/10.1086/626835	journal	July 1962
A stochastic diffusion process for the Dirichlet distribution Bakosi, J.; Ristorcelli, J. R. arXiv https://doi.org/10.48550/arxiv.1303.0217	text	January 2013
Applications of the Dirichlet distribution to forensic match probabilities Lange, Kenneth Genetica, Vol. 96, Issue 1-2 https://doi.org/10.1007/BF01441156	journal	June 1995
Generalized Dirichlet distribution in Bayesian analysis Wong, Tzu-Tsung Applied Mathematics and Computation, Vol. 97, Issue 2-3 https://doi.org/10.1016/S0096-3003(97)10140-0	journal	December 1998
Multivariate Jacobi process with application to smooth transitions Gourieroux, Christian; Jasiak, Joann Journal of Econometrics, Vol. 131, Issue 1-2 https://doi.org/10.1016/j.jeconom.2005.01.014	journal	March 2006
An explicit transition density expansion for a multi-allelic Wright–Fisher diffusion with general diploid selection Steinrücken, Matthias; Wang, Y. X. Rachel; Song, Yun S. Theoretical Population Biology, Vol. 83 https://doi.org/10.1016/j.tpb.2012.10.006	journal	February 2013
Assumed β-pdf Model for Turbulent Mixing: Validation and Extension to Multiple Scalar Mixing Girimaji, S. S. Combustion Science and Technology, Vol. 78, Issue 4-6 https://doi.org/10.1080/00102209108951748	journal	August 1991
Concepts of Independence for Proportions with a Generalization of the Dirichlet Distribution Connor, Robert J.; Mosimann, James E. Journal of the American Statistical Association, Vol. 64, Issue 325 https://doi.org/10.1080/01621459.1969.10500963	journal	March 1969
Exploring the beta distribution in variable-density turbulent mixing Bakosi, J.; Ristorcelli, J. R. Journal of Turbulence, Vol. 11 https://doi.org/10.1080/14685248.2010.510843	journal	January 2010
An approximation to the multinomial distribution some properties and applications Johnson, N. L. Biometrika, Vol. 47, Issue 1-2 https://doi.org/10.1093/biomet/47.1-2.93	journal	January 1960
On the compound multinomial distribution, the multivariate β-distribution, and correlations among proportions Mosimann, James E. Biometrika, Vol. 49, Issue 1-2 https://doi.org/10.1093/biomet/49.1-2.65	journal	January 1962
Bayesian methods for categorical data under informative general censoring Paulino, Carlos Daniel Mimoso; De BraganÇA Pereira, Carlos Alberto Biometrika, Vol. 82, Issue 2 https://doi.org/10.1093/biomet/82.2.439	journal	January 1995
Mathematical contributions to the theory of evolution.—On a form of spurious correlation which may arise when indices are used in the measurement of organs Pearson, Karl Proceedings of the Royal Society of London, Vol. 60, Issue 359-367, p. 489-498 https://doi.org/10.1098/rspl.1896.0076	journal	January 1897
The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes Forman, Julie Lyng; SØRensen, Michael Scandinavian Journal of Statistics, Vol. 35, Issue 3 https://doi.org/10.1111/j.1467-9469.2007.00592.x	journal	September 2008
A Stochastic Diffusion Process for the Dirichlet Distribution Bakosi, J.; Ristorcelli, J. R. International Journal of Stochastic Analysis, Vol. 2013 https://doi.org/10.1155/2013/842981	journal	April 2013
Geochronology of pluvial Lake Cochise, southern Arizona; [Part] 3, Pollen statistics and Pleistocene metastability Martin, P. S.; Mosimann, J. E. American Journal of Science, Vol. 263, Issue 4 https://doi.org/10.2475/ajs.263.4.313	journal	April 1965

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Diffusion Processes Satisfying a Conservation Law Constraint Bakosi, J.; Ristorcelli, J. R. International Journal of Stochastic Analysis, Vol. 2014 https://doi.org/10.1155/2014/603692	journal	March 2014

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Fokker-Planck equation
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References (16)

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