Reconstructing a random scenery observed with random errors along a random walk path

• 成果类型: Article
• 署名作者: Heinrich, M; Rolles, SWW
• 署名单位: University of Bielefeld; University of California System; University of California Los Angeles
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400-003-0257-3
• 发表日期: 2003
• 页码: 539-577
• 关键词: mixing properties

摘要

We show that an i.i.d. uniformly colored scenery on Z observed along a random walk path with bounded jumps can still be reconstructed if there are some errors in the observations. We assume the random walk is recurrent and can reach every point with positive probability. At time k, the random walker observes the color at her present location with probability 1 - delta and an error Y-k with probability delta. The errors Y-k, k greater than or equal to 0, are assumed to be stationary and ergodic and independent of scenery and random walk. If the number of colors is strictly larger than the number of possible jumps for the random walk and delta is sufficiently small, then almost all sceneries can be almost surely reconstructed up to translations and reflections.