The law of large numbers and the law of the iterated logarithm for infinite dimensional interacting diffusion processes

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	The law of large numbers and the law of the iterated logarithm for infinite dimensional interacting diffusion processes
	Schmuland, B ; Sun, W
	2003-09-01
发表期刊	INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS
ISSN	0219-0257
卷号	6 期号:3 页码:489-503
摘要	The classical Dirichlet form given by the intrinsic gradient on Gamma(R)d is associated with a Markov process consisting of a countable family of interacting diffusions. By considering each diffusion as a particle with unit mass, the randomly evolving configuration can be thought of as a Radon measure valued diffusion. The quasi-sure analysis of Dirichlet forms is used to find exceptional sets of configurations for this Markov process. We consider large scale properties of the configuration and show that, for quite general measures, the process never hits those unusual configurations that violate the law of large numbers. Furthermore, for certain Gibbs measures, which model random particles in R-d that interact via a potential function, we show, for d = 1, 2, that the process never hits those unusual configurations that violate the law of the iterated logarithm.
关键词	configuration space Dirichlet form law of large numbers law of the iterated logarithm
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical ; Statistics & Probability
WOS记录号	WOS:000186719600007
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18714
专题	中国科学院数学与系统科学研究院
通讯作者	Schmuland, B
作者单位	1.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 2.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Schmuland, B,Sun, W. The law of large numbers and the law of the iterated logarithm for infinite dimensional interacting diffusion processes[J]. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS,2003,6(3):489-503.
APA	Schmuland, B,&Sun, W.(2003).The law of large numbers and the law of the iterated logarithm for infinite dimensional interacting diffusion processes.INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS,6(3),489-503.
MLA	Schmuland, B,et al."The law of large numbers and the law of the iterated logarithm for infinite dimensional interacting diffusion processes".INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS 6.3(2003):489-503.