Monotonicity and robustness in Wiener disorder detection

TL;DR

This paper investigates the detection of drift changes in Brownian motion, focusing on monotonicity and robustness properties under model extensions, including random post-change drifts and misspecification effects.

Contribution

It introduces new monotonicity and robustness analyses for Wiener disorder detection with extended models, including random drifts and model misspecification.

Findings

Monotonicity properties depend on model parameters.

Robustness to model misspecification is characterized.

Extensions to classical detection problems are provided.

Abstract

We study the problem of detecting a drift change of a Brownian motion under various extensions of the classical case. Specifically, we consider the case of a random post-change drift and examine monotonicity properties of the solution with respect to different model parameters. Moreover, robustness properties -- effects of misspecification of the underlying model -- are explored.