ASYMPTOTIC PROPERTIES OF CUSUM AND SHIRYAEV'S PROCEDURES FOR DETECTING A CHANGE IN A NONHOMOGENEOUS GAUSSIAN PROCESS

Suppose one can observe a Gaussian nonhomogeneous process with a continuous time parameter. At an unknown time the observed process may leave its standard state, the drift of the process changes and becomes equal to a nonrandom function. Subject to a restriction on the rate of false alarms, one wants to detect the change \as soon as possible". We investigate Page's and Shiryaev's sequential detection procedures for essentially nonhomogeneous case. Inequalities and asymptotic approximations for the operating characteristics of these procedures are presented. The relative eeciency of the procedures is obtained for \asymptotic power nonhomogeneity".

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