Abstract
The problem of the sequential detection of a change in the drift of a one-dimensional Brownian motion is considered under the assumptions that the detection must eventually occur within a finite horizon and the detection delay is exponentially penalized. Our results extend those obtained by Beibel for the infinite horizon sequential detection with exponential penalty (Ann Stat 28:1696-1701, 2000) and by Gapeev and Peskir for the finite horizon sequential detection with linear penalty (Stoch Process Appl 116:1770-1791, 2006).
Lingua originale | English |
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pagine (da-a) | 224-238 |
Numero di pagine | 15 |
Rivista | Journal of Optimization Theory and Applications |
Volume | 198 |
DOI | |
Stato di pubblicazione | Pubblicato - 2023 |
Keywords
- Brownian motion
- Exponential penalty
- Sequential detection
- Optimal stopping
- Sequential analysis
- Finite horizon