| 退化扩散过程的经验测度的大偏差定理 |
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| 引用本文： | 刘秀芹,席福宝. 退化扩散过程的经验测度的大偏差定理[J]. 北京理工大学学报(英文版), 2001, 10(3): 233-239 |
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| 作者姓名： | 刘秀芹 席福宝 |
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| 作者单位： | 北京理工大学应用数学系, |
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| 摘 要： | Xε(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μ在Rr-n上的投影测度ν的大偏差定理.
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| 关 键 词： | 经验测度 大偏差 扩散过程 |
| 收稿时间： | 2000-06-20 |
Large Deviation Theorem for Empirical Measures of Degenerate Diffusion Processes |
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| LIU Xiu qin and XI Fu bao. Large Deviation Theorem for Empirical Measures of Degenerate Diffusion Processes[J]. Journal of Beijing Institute of Technology, 2001, 10(3): 233-239 |
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| Authors: | LIU Xiu qin and XI Fu bao |
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| Affiliation: | Dept. of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China;Dept. of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | A class of multi-dimensional degenerate diffusion processes Xε(t) in Rr(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here Xε(t) saitisfies the stochastic differential equation dXε(t)=σ(Xε(t))dW(t)+B(Xε(t))dt+εσ～(Xε(t))dW(t),ε＞0. Xε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t))dW(t)+B(X(t))dt. A large deviation theorem for projection measures ν on Rr-n(n＜r) of empirical measures μ are proved. |
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| Keywords: | ; ; |
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