Martin boundary of a reflected random walk on a half-space

• 成果类型: Article
• 署名作者: Ignatiouk-Robert, Irina
• 署名单位: CY Cergy Paris Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0228-4
• 发表日期: 2010
• 页码: 197-245
• 关键词: large deviations; discontinuous statistics; MARKOV-PROCESSES

摘要

The complete representation of the Martin compactification for reflected random walks on a half-space Z(d) x N is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the radial compactification obtained by Ney and Spitzer for the homogeneous random walks in Zd : convergence of a sequence of points z(n) is an element of Z(d-1) x N to a point of on the Martin boundary does not imply convergence of the sequence z(n)/vertical bar z(n)vertical bar on the unit sphere S-d. Our approach relies on the large deviation properties of the scaled processes and uses Pascal's method combined with the ratio limit theorem. The existence of non-radial limits is related to non-linear optimal large deviation trajectories.