| A Nonstandard Levy-Khintchine Formula and Levy Processes |
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| 引用本文： | Siu Ah NG. A Nonstandard Levy-Khintchine Formula and Levy Processes[J]. 数学学报(英文版), 2008, 24(2): 241-252. DOI: 10.1007/s10114-007-1024-7 |
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| 作者姓名： | Siu Ah NG |
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| 作者单位： | School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209, South Africa |
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| 基金项目： | Work completed at BiBoS Universitat Bielefeld in 2004 with support from Norway-SA Grant 2067063, acknowledged with gratitude |
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| 摘 要： | We use methods from nonstandard analysis to obtain a short and simple derivation of the Levy-Khintchine formula via an explicit construction of certain laws of the infinitesimal increments. Consequently, any arbitrary Levy process is representable as the standard part of a hyperfinite sum of infinitesimal increments.
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| 关 键 词： | 非标准分析 无穷小 超有限 利维过程 |
| 文章编号： | 10.1007/s10114-007-1024-7 |
| 收稿时间： | 2005-09-08 |
| 修稿时间： | 2006-06-05 |
A nonstandard Lévy-Khintchine formula and Lévy processes |
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| Siu Ah Ng. A nonstandard Lévy-Khintchine formula and Lévy processes[J]. Acta Mathematica Sinica(English Series), 2008, 24(2): 241-252. DOI: 10.1007/s10114-007-1024-7 |
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| Authors: | Siu Ah Ng |
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| Affiliation: | (1) School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209, South Africa |
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| Abstract: | We use methods from nonstandard analysis to obtain a short and simple derivation of the Levy-Khintchine formula via an explicit construction of certain laws of the infinitesimal increments. Consequently, any arbitrary Levy process is representable as the standard part of a hyperfinite sum of infinitesimal increments. |
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| Keywords: | Levy processes Levy-Khintchine formula nonstandard analysis infinitesimal hyperfinite |
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