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 -