PREDICTABILITY AND STOPPING ON LATTICES OF SETS

• 成果类型: Article
• 署名作者: IVANOFF, BG; MERZBACH, E; SCHIOPUKRATINA, I
• 署名单位: Bar Ilan University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01192958
• 发表日期: 1993
• 页码: 433-446
• 关键词: partially ordered sets; random-fields

摘要

As a first step in the development of a general theory of set-indexed martingales, we define predictability on a general space with respect to a filtration indexed by a lattice of sets. We prove a characterization of the predictable sigma-algebra in terms of adapted and ''left-continuous'' processes without any form of topology for the index set. We then define a stopping set and show that it is a natural generalization of the stopping time; in particular, the predictable sigma-algebra can be characterized by various stochastic intervals generated by stopping sets.