Large Deviation Theorem for Empirical Measures of Degenerate Diffusion Processes  

退化扩散过程的经验测度的大偏差定理(英文)

作　　者：刘秀芹[1] 席福宝[1] 

机构地区：[1]北京理工大学应用数学系,北京100081

出　　处：《Journal of Beijing Institute of Technology》2001年第3期233-239,共7页北京理工大学学报（英文版）

摘　　要：A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are provedXε(t)是Rr(r≥ 2 )上退化扩散过程X(t)的小随机扰动 ,其中X(t)满足随机微分方程dX(t) =σ(X(t) )dW (t) +B(X(t) )dt;Xε(t)满足随机微分方程dXε(t) =σ(Xε(t) )dW (t) +B(Xε(t) )dt+εσ(Xε(t) )dW (t) ,ε >0 .通过研究Rr 上的一类多维退化扩散过程Xε(t)的经验测度的渐近性质 ,证明了Xε(t)的经验测度

关 键 词：empirical measures large deviation diffusion process 

分 类 号：O211.63[理学—概率论与数理统计]