The optional stopping theorem for quantum martingales
The optional stopping theorem for quantum martingales
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DOI：
10.1016/j.jfa.2006.04.012
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发表时间：
2006-09
影响因子：
1.7
通讯作者：
Agnès Coquio
中科院分区：
文献类型：
--
作者：
Agnès Coquio
In classical probability theory, a random time T is a stopping time in a filtration [Formula: see text] if and only if the optional sampling holds at T for all bounded martingales. Furthermore, if a process [Formula: see text] is progressively measurable with respect to [Formula: see text] , then XTis FT-measurable. Unfortunately, this is not the case in noncommutative probability with the definition of stopped process used until now. It is shown in this article that we can define the stopping of noncommutative processes in Fock space in such a way that all the bounded martingales can be stopped at any stopping time T, are adapted to the filtration of the past before T and satisfy the optional stopping theorem.
