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.
Original language | English |
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Journal | Stochastic Processes and Their Applications |
Volume | 150 |
Pages (from-to) | 1068-1090 |
ISSN | 0304-4149 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
Publisher Copyright:
© 2021 Elsevier B.V.
- Brownian motion, Free-boundary problem, Optimal stopping, Parabolic partial differential equation, Random drift, Sequential testing
Research areas
ID: 276952971