Detection of multiple changes in the mean of a random process

In this Note, general results on the off-line least-square estimate of changes in the mean of a stationary random process are presented. To reach this goal, a generalisation of the Hájek-Rényi inequality, dealing with the functuation of the normalized partial sums, is given: it applies to a very large class of processes. This result is used to derive the consistence and the rate of convergence of the change-point estimate, no matter if the number of changes is known or not. All these results apply to a large class of stationary processes, including strongly mixing and long-range dependent processes.