A Posteriori Change-Point Problems
In this chapter, a posteriori change-point problems are considered. As was already mentioned in Chapter 2, the a posteriori change-point problem can be formulated in the following way: given a realisation of a random sequence X, the hypothesis of its stochastic homogeneity has to be proved. If this hypothesis is rejected, then estimates of change-points have to be obtained. Following the abovementioned general approach to disorder detection (see 2.4), almost everywhere in this chapter a posteriori change-point problems are considered in a standard situation when an unknown shift of the mean value of a random sequence X occurs (other changing characteristics of distributions are considered as nuisance parameters).
KeywordsStandard Wiener Process Functional Limit Theorem Stochastic Homogeneity Continuous Random Process Independent Standard Wiener Process
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