On discrete time ergodic filters with wrong initial data

• 成果类型: Article
• 署名作者: Kleptsyna, M. L.; Veretennikov, A. Yu.
• 署名单位: University of Leeds; Le Mans Universite; Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-007-0089-7
• 发表日期: 2008
• 页码: 411-444
• 关键词: Exponential stability; nonlinear filters; asymptotic stability; approximation

摘要

For a class of non-uniformly ergodic Markov chains (X-n) satisfying exponential or polynomial beta-mixing, under observations (Y-n) subject to an IID noise with a positive density, it is shown that wrong initial data is forgotten in the mean total variation topology, with a certain exponential or polynomial rate.