Recognising the last record of sequence. (English) Zbl 1156.60025
The best-choice problem can be formulated in terms of embedded process of records, because the overall extreme is the last record observation. In the paper the occurrence of records is modeling by means of a nonincreasing right-continuous Markov process \(R=(R_t, t\geq 0)\) with the following type of behavior: given the current state is \(r>0\), the process jumps at rate \(r\) to a new state \(rX\), where \(X\) has an arbitrary distribution on the unit interval. They construct the optimal policy \(\pi_s\) which prescribes stopping at the first record time when \((T-t)R_t\leq s\) holds and in special case of parametric family of problems derive an explicit formula for the maximum probability of recognizing the last record.
Reviewer: Vladimir Mazalov (Petrozavodsk)
MSC:
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
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