Why does the elephant random walk behave as the randomized play- the-winner rule?
报告专家：张立新（浙江工商大学 & 浙江大学）
报告时间：2024年7月25日（星期四）下午14：30-15：30
报告地点：数学学院西303报告厅
报告摘要：The randomized play-the-winner rule (RPW) is a response-adaptive design proposed by Wei and Durham (1978) for sequentially randomizing patients to treatments in a two-treatment clinical trial so that more patients are assigned to the better treatment as the clinical trial goes on. The elephant random walk (ERW) proposed by Schutz and Trimper (2004) is a non-Markovian discrete-time random walk that has a link to a famous saying that elephants can always remember where they have been. The asymptotic behaviors of RPW rule and ERW have been studied in litterateurs independently, and their asymptotic behaviors are very similar. We present the link between the ERW and the RPW rule by the recursive stochastic algorithm. With the help of the recursive stochastic algorithm, we obtain the strong invariance principle of multi-dimensional varying-memory ERW with random step sizes. The precise law of the iterated logarithm and the Chung-type law of the iterated logarithm are obtained by applying the strong invariance principle.
专家简介：张立新，浙江工商大学特聘教授，浙江大学求是特聘教授。1995年获复旦大学理学博士学位， 1997年晋升为教授，2001年起先后担任浙江大学统计学研究所副所长、常务副所长、所长，浙江大学数学系副主任、数学科学学院副院长。现任浙江大学数据科学研究中心副主任、中国现场统计研究会常务理事、浙江省现场统计研究会理事长。主要从事临床试验自适应随机化设计、概率极限理论、相依数据模型等领域的研究，发表了学术论文170余篇，先后主持国家自然科学基金面上项目5项、杰出青年基金项目1项、重点项目1项、联合基金重点项目1项，于2008年入选教育部“新世纪优秀人才支持计划”，2018年入选浙江省科技创新领军人才，2020年当选Institute of Mathematical Statistics的 Fellow。
邀请人：连增 胡泽春
