| 车文彬,宋立新,冯敬海,鲁大伟.在无界凸区域上多个布朗运动之和首冲时[J].,2012,(2):309-312 |
| 在无界凸区域上多个布朗运动之和首冲时 |
| The first exit time of sum of Brownian motions from unbounded convex domain |
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| DOI：10.7511/dllgxb201202025 |
| 中文关键词: Bessel函数 首冲时 Slepian不等式 布朗运动 渐近估计 |
| 英文关键词: Bessel function the first exit time Slepian′s inequality Brownian motion asymptotic estimates\@ |
| 基金项目:国家自然科学基金资助项目(61175041,11101061);大连理工大学前沿交叉学科基金资助项目(DUT10JS06);高等学校博士学科点专项科研基金资助项目(2010041110036). |
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| 中文摘要: |
| 考虑在无界区域中Bessel函数下多个布朗运动和的首冲时问题．介绍了利用高斯计算技巧和Slepian不等式得到的单个布朗运动在无界开区域 R d+1 中首冲时的上 下界的渐近估计,然后考虑了多个布朗运动的和在Bessel函数下首冲时的上 下界渐近估计．首先考虑在移动边界下的首冲时问题,之后再推广到无界区域中多个布朗运动的和．说明单个的布朗运动首冲时问题,可以推广到多个布朗运动之和的首冲时问题． |
| 英文摘要: |
| The first exit time of the sum of several Brownian motions in the case of Bessel function from an unbounded domain is considered. Firstly, general upper and lower asymptotic estimates for the first exit time of one Brownian motion from an unbounded open domain R d+1 are obtained, which are based on a powerful Gaussian technique and Slepian′s inequality. Then, the general upper and lower asymptotic estimates are considered to the first exit time of the sum of several Brownian motions in the case of Bessel function. At first, the first exit time probability with moving boundary is considered, then, it′s extended to the sum of the number of Brownian motions in the unbounded domain. It means that the first exit time of one Brownian motion is suitable for the first exit time of the sum of several Brownian motions. |
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