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).
Buonaguidi, B., Finite Horizon Sequential Detection with Exponential Penalty for the Delay, <<JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS>>, 2023; 198 (1): 224-238. [doi:10.1007/s10957-023-02239-8] [https://hdl.handle.net/10807/271321]
Finite Horizon Sequential Detection with Exponential Penalty for the Delay
Buonaguidi, Bruno
2023
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).
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
