Skorokhod embeddings for two-sided Markov chains

• 成果类型: Article
• 署名作者: Morters, Peter; Redl, Istvan
• 署名单位: University of Bath
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0637-5
• 发表日期: 2016
• 页码: 483-508
• 关键词: shifts; head

摘要

Let (X-n : n is an element of Z) be a two-sided recurrent Markov chain with fixed initial state and let be a probability measure on its state space. We give a necessary and sufficient criterion for the existence of a non-randomized time T such that has the law of the same Markov chain with initial distribution . In the case when our criterion is satisfied we give an explicit solution, which is also a stopping time, and study its moment properties. We show that this solution minimizes the expectation of in the class of all non-negative solutions, simultaneously for all non-negative concave functions psi.