Detecting the presence of a random drift in Brownian motion
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Detecting the presence of a random drift in Brownian motion. / Johnson, P.; Pedersen, J. L.; Peskir, G.; Zucca, C.
I: Stochastic Processes and Their Applications, Bind 150, 2022, s. 1068-1090.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Detecting the presence of a random drift in Brownian motion
AU - Johnson, P.
AU - Pedersen, J. L.
AU - Peskir, G.
AU - Zucca, C.
N1 - Publisher Copyright: © 2021 Elsevier B.V.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Brownian motion
KW - Free-boundary problem
KW - Optimal stopping
KW - Parabolic partial differential equation
KW - Random drift
KW - Sequential testing
U2 - 10.1016/j.spa.2021.05.006
DO - 10.1016/j.spa.2021.05.006
M3 - Journal article
AN - SCOPUS:85109096935
VL - 150
SP - 1068
EP - 1090
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
ER -
ID: 276952971