Change detection for finite dimensional Gaussian linear systems - a bound for the almost sure false alarm rate

We consider the problem of change detection in the context of finite dimensional Gaussian linear systems. In particular a known initial system will be tested for eventual changes against a known alternative using a simplified version of the Page-Hinkley or CUSUM detector. We show that the detector is L-mixing, implying the existence of an almost sure false alarm rate. The derivation of an explicit upper bound for the latter will be outlined.