  In this paper, we study the quickest change detection with mismatched
post-change models. A change point is the time instant at which the
distribution of a random process changes. The objective of quickest change
detection is to minimize the detection delay of an unknown change point under
certain performance constraints, such as average run length (ARL) to false
alarm or probability of false alarm (PFA). Most existing change detection
procedures assume perfect knowledge of the random process distributions before
and after the change point. However, in many practical applications such as
anomaly detection, the post-change distribution is often unknown and needs to
be estimated with a limited number of samples. In this paper, we study the case
that there is a mismatch between the true post-change distribution and the one
used during detection. We analytically identify the impacts of mismatched
post-change models on two classical detection procedures, the cumulative sum
(CUSUM) procedure and the Shiryaev-Roberts (SR) procedure. The impacts of
mismatched models are characterized in terms of various finite or asymptotic
performance bounds on ARL, PFA, and average detection delay (ADD). It is shown
that post-change model mismatch results in an increase in ADD, and the rate of
performance degradation depends on the difference between two Kullback-Leibler
(KL) divergences, one is between the priori- and post-change distributions, and
the other one is between the true and mismatched post-change distributions.
