Quickest real-time detection of a Brownian coordinate drift

Minimax Optimality of Shiryaev-Roberts Procedure for Quickest Drift Change Detection of a Brownian motion

The problem of detecting a change in the drift of a Brownian motion is considered. The change point is assumed to have a modified exponential prior distribution with unknown parameters. A worst-case analysis with respect to these parameters is adopted leading to a min-max problem formulation. Analytical and numerical justifications are provided towards establishing that the Shiryaev-Roberts pro...

Quickest Detection of Drift Change for Brownian Motion in Generalized Bayesian and Minimax Settings

The paper deals with the quickest detection of a change of the drift of the Brownian motion. We show that the generalized Bayesian formulation of the quickest detection problem can be reduced to the optimal stopping problem for a diffusion Markov process. For this problem the optimal procedure is described and its characteristics are found. We show also that the same procedure is asymptotically...

Real-time financial surveillance via quickest change-point detection methods

On Asymptotic Optimality of the Second Order in the Minimax Quickest Detection Problem of Drift Change for Brownian Motion∗

This paper deals with the minimax quickest detection problem of a drift change for the Brownian motion. The following minimax risks are studied: C(T ) = infτ∈MT supθ Eθ(τ−θ | τ θ) and C(T ) = inf τ∈MT supθ Eθ(τ − θ | τ θ), where MT is the set of stopping times τ such that E∞τ = T and MT is the set of randomized stopping times τ such that E∞τ = T . The goal of this paper is to obtain for these r...

Quickest Search over Brownian Channels

In this paper we resolve an open problem proposed by [9]. Consider a sequence of Brownian Motions with unknown drift equal to one or zero, which may be observed one at a time. We give a procedure for finding, as quickly as possible, a process which is a Brownian Motion with nonzero drift. This original quickest search problem, in which the filtration itself is dependent on the observation strat...