Measuring the range of an additive Levy process

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	Measuring the range of an additive Levy process
	Khoshnevisan, D ; Xiao, YM ; Zhong, YQ
	2003-04-01
发表期刊	ANNALS OF PROBABILITY
ISSN	0091-1798
卷号	31 期号:2 页码:1097-1141
摘要	The primary goal of this paper is to study the range of the random field X (t) = Sigma(j=1)(N) X(j) (t(j)), where X(1),...,X(N) are independent Levy processes in R(d). To cite a typical result of this paper, let us suppose that psi(i) denotes the Levy exponent of X(i) for each i = 1,...,N. Then, under certain mild conditions, we show that a necessary and sufficient condition for X(RN) to have positive d-dimensional Lebesgue measure is the integrability of the function R(d) There Exists xi bar right arrow Pi(J=1)(N) Re{1 + psi(j)(xi)}(-1). This extends a celebrated result of Kesten and of Bretagnolle in the one-parameter setting. Furthermore, we show that the existence of square integrable local times is yet another equivalent condition for the mentioned integrability criterion. This extends a theorem of Hawkes to the present random fields setting and completes the analysis of local times for additive Levy processes initiated in a companion by paper Khoshnevisan, Xiao and Zhong.
关键词	additive Levy processes strictly stable processes capacity energy local times Hausdorff dimension
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000182167600021
出版者	INST MATHEMATICAL STATISTICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18542
专题	中国科学院数学与系统科学研究院
通讯作者	Khoshnevisan, D
作者单位	1.Univ Utah, Dept Math, Salt Lake City, UT 84112 USA 2.Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA 3.Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Khoshnevisan, D,Xiao, YM,Zhong, YQ. Measuring the range of an additive Levy process[J]. ANNALS OF PROBABILITY,2003,31(2):1097-1141.
APA	Khoshnevisan, D,Xiao, YM,&Zhong, YQ.(2003).Measuring the range of an additive Levy process.ANNALS OF PROBABILITY,31(2),1097-1141.
MLA	Khoshnevisan, D,et al."Measuring the range of an additive Levy process".ANNALS OF PROBABILITY 31.2(2003):1097-1141.