Diffusion Processes Satisfying a Conservation Law Constraint

Bakosi, J.; Ristorcelli, J. R.

doi:10.1155/2014/603692

Diffusion Processes Satisfying a Conservation Law Constraint

Journal Article · Mon Mar 03 23:00:00 EST 2014 · International Journal of Stochastic Analysis

DOI:https://doi.org/10.1155/2014/603692· OSTI ID:1233162

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

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequences of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.

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:: 1233162

Report Number(s):: LA-UR--13-28548

Journal Information:: International Journal of Stochastic Analysis, Journal Name: International Journal of Stochastic Analysis Vol. 2014; ISSN 2090-3332

Publisher:: HindawiCopyright Statement

Country of Publication:: United States

Language:: English

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