 Some fluctuation results for weakly interacting multi-type particle systemsAmarjit Budhiraja and Ruoyu Wu Stochastic Processes and their Applications, 2016, vol. 126, issue 8, 2253-2296 Abstract: A collection of N-diffusing interacting particles where each particle belongs to one of K different populations is considered. Evolution equation for a particle from population k depends on the K empirical measures of particle states corresponding to the various populations and the form of this dependence may change from one population to another. In addition, the drift coefficients in the particle evolution equations may depend on a factor that is common to all particles and which is described through the solution of a stochastic differential equation coupled, through the empirical measures, with the N-particle dynamics. We are interested in the asymptotic behavior as N→∞. Although the full system is not exchangeable, particles in the same population have an exchangeable distribution. Using this structure, one can prove using standard techniques a law of large numbers result and a propagation of chaos property. In the current work we study fluctuations about the law of large number limit. For the case where the common factor is absent the limit is given in terms of a Gaussian field whereas in the presence of a common factor it is characterized through a mixture of Gaussian distributions. We also obtain, as a corollary, new fluctuation results for disjoint sub-families of single type particle systems, i.e. when K=1. Finally, we establish limit theorems for multi-type statistics of such weakly interacting particles, given in terms of multiple Wiener integrals. Keywords: Mean field interaction; Common factor; Weakly interacting diffusions; Propagation of chaos; Central limit theorems; Fluctuation limits; Exchangeability; Symmetric statistics; Multiple Wiener integrals (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:8:p:2253-2296 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2016.01.010 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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