Some fluctuation results for weakly interacting multi-type particle systems

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• 作者：Amarjit Budhiraja ; ^{budhiraj@email.unc.edu" class="auth_mail" title="E-mail the corresponding author} ; Ruoyu Wu ^{wuruoyu@live.unc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60F05 ; 60K35 ; 60H30 ; 60J70
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：126
• 期：8
• 页码：2253-2296
• 全文大小：452 K

文摘

A collection of N$N$-diffusing interacting particles where each particle belongs to one of K$K$ different populations is considered. Evolution equation for a particle from population 70570c363aefe38c39b39f344d2e52aa" title="Click to view the MathML source">k$k$ depends on the K$K$ 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$N$-particle dynamics. We are interested in the asymptotic behavior as N→∞$N\to \infty$. 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$K=1$. Finally, we establish limit theorems for multi-type statistics of such weakly interacting particles, given in terms of multiple Wiener integrals.