A Bayesian sequential test for the drift of a fractional Brownian motion

We consider a fractional Brownian motion with linear drift such that its unknown drift coefficient has a prior normal distribution and construct a sequential test for the hypothesis that the drift is positive versus the alternative that it is negative. We show that the problem of constructing the te...

Full description

Saved in:
Bibliographic Details
Published in:Advances in applied probability 2020-12, Vol.52 (4), p.1308-1324
Main Authors: Muravlev, Alexey, Zhitlukhin, Mikhail
Format: Article
Language:English
Subjects:
Brownian motion
Drift
Hypotheses
Integral equations
Normal distribution
Original Article
Original Articles
Probability
Random variables
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a fractional Brownian motion with linear drift such that its unknown drift coefficient has a prior normal distribution and construct a sequential test for the hypothesis that the drift is positive versus the alternative that it is negative. We show that the problem of constructing the test reduces to an optimal stopping problem for a standard Brownian motion obtained by a transformation of the fractional Brownian motion. The solution is described as the first exit time from some set, and it is shown that its boundaries satisfy a certain integral equation, which is solved numerically.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2020.43