Detecting the presence of a random drift in Brownian motion

P. Johnson, J.L. Pedersen, G. Peskir and C. Zucca

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 1068-1090

Abstract: Consider a standard Brownian motion in one dimension, having either a zero drift, or a non-zero drift that is randomly distributed according to a known probability law. Following the motion in real time, the problem is to detect as soon as possible and with minimal probabilities of the wrong terminal decisions, whether a non-zero drift is present in the observed motion. We solve this problem for a class of admissible laws in the Bayesian formulation, under any prior probability of the non-zero drift being present in the motion, when the passage of time is penalised linearly.

Keywords: Sequential testing; Brownian motion; Random drift; Optimal stopping; Parabolic partial differential equation; Free-boundary problem (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2021.05.006

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