The optional sampling theorem for submartingales in the sequentially planned context. (English) Zbl 1114.62078
Summary: The optional sampling theorem is considered in a sequentially planned context. We prove the optional sampling theorem for direct successors and for sampling plans with a finite number of stages. Also, the theorem is studied in the general case under a uniform integrability condition; we obtain it for submartingales with a last element, and for submartingales that verify a bounded condition based on uniform integrability.
MSC:
| 62L10 | Sequential statistical analysis |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 60G48 | Generalizations of martingales |
References:
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