Detecting the presence of a random drift in Brownian motion

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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.

OriginalsprogEngelsk
TidsskriftStochastic Processes and Their Applications
Vol/bind150
Sider (fra-til)1068-1090
ISSN0304-4149
DOI
StatusUdgivet - 2022

Bibliografisk note

Funding Information:
The authors are grateful to Patrizia Tavella for insightful discussions on the problem studied in the paper in relation to the global navigation satellite system Galileo. This work was supported by a research grant ( 17617 ) from Villum Fonden .

Publisher Copyright:
© 2021 Elsevier B.V.

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