BOUNDS ON THE SPEED AND ON REGENERATION TIMES FOR CERTAIN PROCESSES ON REGULAR TREES

• 成果类型: Article
• 署名作者: Collevecchio, Andrea; Schmitz, Tom
• 署名单位: Universita Ca Foscari Venezia; Max Planck Society
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP719
• 发表日期: 2011
• 页码: 1073-1101
• 关键词: transient random-walks; reinforced random-walk; biased random-walks; random environment; large deviations; LIMIT-THEOREMS

摘要

We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic [Probab. Theory Related Fields. 122 (2002) 567-592] prove an upper bound of the form b/(b + delta) for the speed on the b-ary tree, where d is the reinforcement parameter. For delta > 1 we provide a lower bound of the form gamma(2)b/(b + delta), where gamma is the survival probability of an associated branching process.