| 近临界紧邻随机游动局部时的重整化极限 |
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| 引用本文： | 周珂,刘敏之.近临界紧邻随机游动局部时的重整化极限[J].北京师范大学学报(自然科学版),2017,53(4):391-394. |
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| 作者姓名： | 周珂 刘敏之 |
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| 作者单位： | 对外经济贸易大学统计学院,100029,北京;北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,100875,北京 |
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| 基金项目： | 国家自然科学基金数学天元基金资助项目，国家自然科学基金资助项目，中央高校基本科研业务费专项资金资助项目 |
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| 摘 要： | Lamperti于1961年证明了在适当条件下, 半直线上一类近临界的紧邻随机游动经过重整化会弱收敛到布朗运动. 考虑过程局部时重整化的极限问题, 运用随机游动的内蕴分枝结构以及非时齐分枝过程重整化极限的结果, 证明了其局部时经过适当的重整化会收敛到布朗运动的局部时.
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| 关 键 词： | 随机游动 近临界 局部时 重整化 |
Scaling limit in local time of near-critical nearest random walk |
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| ZHOU Ke,LIU Minzhi.Scaling limit in local time of near-critical nearest random walk[J].Journal of Beijing Normal University(Natural Science),2017,53(4):391-394. |
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| Authors: | ZHOU Ke LIU Minzhi |
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| Institution: | 1)School of Statistics,University of International Business and Economics,100029,Beijing,China;
2)School of Mathematical Sciences,Key Laboratory of Mathematics and Complex Systems of Ministry of Education,Beijing Normal University,100875,Beijing,China |
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| Abstract: | In 1961,Lamperti proves that a sequence of certain near-critical nearest random walks converges weakly to Brownian motion after proper scaling.Scaling limit in local times is then considered.We prove that local times converge to those of Brownian motion by corresponding scaling.Our proof is based on intrinsic branching structure of random walk and convergence of time in homogeneous branching processe. |
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| Keywords: | random walk near-critical local time scaling |
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