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.

Detecting the presence of a random drift in Brownian motion

Zucca C.
2021

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.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
In Press
0
1
https://www.sciencedirect.com/science/article/pii/S0304414921000909
Brownian motion; Free-boundary problem; Optimal stopping; Parabolic partial differential equation; Random drift; Sequential testing
Johnson P.; Pedersen J.L.; Peskir G.; Zucca C.
File in questo prodotto:
File Dimensione Formato  
SPA_Preprint2021Paper-Accepted-17.5.21.pdf

embargo fino al 06/06/2023

Tipo di file: POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione 276.44 kB
Formato Adobe PDF
276.44 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1847650
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact