Processes with long memory: Regenerative construction and perfect simulation

• 成果类型: Article
• 署名作者: Comets, F; Fernández, R; Ferrari, PA
• 署名单位: Universite Paris Cite; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); Universidade de Sao Paulo
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2002
• 页码: 921-943
• 关键词: markov; systems; THEOREM; chains

摘要

We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence. Even though the process has infinite memory, its value at time 0 depends only on a finite, but random, number of these uniform variables. The algorithm is based on a recent regenerative construction of these measures by Ferrari, Maass, Martinez and Ney. As applications, we discuss the perfect simulation of binary autoregressions and Markov chains on the unit interval.