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.
Buonaguidi, B., Muliere, P., On the martingale and free-boundary approaches in sequential detection problems with exponential penalty for delay, <<STOCHASTICS>>, 2014; 86 (6): 865-869. [doi:10.1080/17442508.2013.865132] [http://hdl.handle.net/10807/133712]
On the martingale and free-boundary approaches in sequential detection problems with exponential penalty for delay
Buonaguidi, Bruno
Primo
;
2014
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.
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