Detection of two-sided alternatives in a Brownian motion model

Change-point detection of two-sided alternatives in the Brownian motion model and its connection to the gambler’s ruin problem with relative wealth perception

A Comparison of 2-CUSUM Stopping Rules for Quickest Detection of Two-sided Alternatives in a Brownian Motion Model

This work compares the performance of all existing 2-CUSUM stopping rules used in the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. As a performance measure an extended Lorden criterion is used. According to this criterion the optimal stopping rule is an equalizer rule. This paper compares the performance of the modified dri...

Optimality of the 2-cusum Drift Equalizer Rules for Detecting Two-sided Alternatives in the Brownian Motion Model

This work employs the Brownian motion model in which observations are taken sequentially. The objective is to detect a two-sided change in the constant drift by means of a stopping rule. As a performance measure, an extended Lorden criterion is used. The goal is to minimize the worst-case detection delay subject to a constraint in the frequency of false alarms. In a companion paper, attention i...

On the Best 2-cusum Stopping Rule for Quickest Detection of Two-sided Alternatives in a Brownian Motion Model∗

This work examines the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. Traditionally, 2-CUSUM stopping rules have been used for this problem due to their asymptotically optimal character as the mean time between false alarms tends to ∞. In particular, attention has focused on 2-CUSUM harmonic mean rules due to the simplicity o...

Investigation of Brownian Motion of CuO-Water Nanofluid in a Porous Cavity with Internal Heat Generation by Using of LTNE Model

In this paper, the effect of the Brownian term in natural convection of CuO-Water nanofluid inside a partially filled porous cavity, with internal heat generation has been studied. It is assumed that the viscosity and thermal conductivity of nanofluid consists of a static part and a Brownian part of which is a function of temperature and the volume fraction of nanofluid. Because of internal hea...