Abstract
We study the connection between the martingale and free-boundary approaches in sequential detection problems for the drift of a Brownian motion, under the assumption of exponential penalty for the delay. By means of the solution of a suitable free-boundary problem, we show that the reward process can be decomposed into the product between a gain function of the boundary point and a positive martingale inside the continuation region.
| Lingua originale | Inglese |
|---|---|
| pagine (da-a) | 865-869 |
| Numero di pagine | 5 |
| Rivista | Stochastics |
| Volume | 86 |
| DOI | |
| Stato di pubblicazione | Pubblicato - 2014 |
Keywords
- Modeling and Simulation
- Statistics and Probability
- free-boundary problem
- martingale approach of Beibel
- optimal stopping
- sequential detection and disorder problems
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