Diffusion Processes Satisfying a Conservation Law Constraint
Joint Authors
Source
International Journal of Stochastic Analysis
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-04
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We investigate coupled stochastic differential equations governing N nonnegative continuous random variables that satisfy a conservation principle.
In various fields a conservation law requires a set of fluctuating variables to be nonnegative 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 nonnegativity and the unit-sum conservation law constraints 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.
American Psychological Association (APA)
Bakosi, J.& Ristorcelli, J. R.. 2014. Diffusion Processes Satisfying a Conservation Law Constraint. International Journal of Stochastic Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-484319
Modern Language Association (MLA)
Bakosi, J.& Ristorcelli, J. R.. Diffusion Processes Satisfying a Conservation Law Constraint. International Journal of Stochastic Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-484319
American Medical Association (AMA)
Bakosi, J.& Ristorcelli, J. R.. Diffusion Processes Satisfying a Conservation Law Constraint. International Journal of Stochastic Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-484319
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-484319