Performance analysis for a changepoint problem

Abstract

Nonlinear stochastic differential equations are used to model a version of the changepoint problem. State estimates of the minimum-mean-square-error type are used in likelihood-ratio tests to detect the time of change. We then evaluate how well the system performs by deriving theoretical expressions for the false alarm probability and a special case of the miss error probability. The approach uses a Fokker-Planck equation. The overall methodology is general and should be of interest in other applications.