Measuring the range of an additive Levy process
文献类型：期刊论文
| 作者 | Khoshnevisan, D; Xiao, YM; Zhong, YQ |
| 刊名 | ANNALS OF PROBABILITY
 |
| 出版日期 | 2003-04-01 |
| 卷号 | 31期号:2页码:1097-1141 |
| 关键词 | additive Levy processes strictly stable processes capacity energy local times Hausdorff dimension |
| ISSN号 | 0091-1798 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000182167600021 |
| 出版者 | INST MATHEMATICAL STATISTICS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/18541]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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