Number of distinct sites visited by a random walk with internal states

• 成果类型: Article
• 署名作者: Nandori, Peter
• 署名单位: Budapest University of Technology & Economics
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0277-8
• 发表日期: 2011
• 页码: 373-403
• 关键词: freedom; range

摘要

In the classical paper of Dvoretzky and ErdAs (Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, pp 353-367, 1951), asymptotics for the expected value and the variance of the number of distinct sites visited by a Simple Symmetric Random Walk were calculated. Here, these results are generalized for Random Walks with Internal States. Moreover, both weak and strong laws of large numbers are proved. As a tool for these results, the error term of the local limit theorem in Kramli and Szasz (Zeitschrift Wahrscheinlichkeitstheorie verw Gebiete 63:85-95, 1983) is also estimated.