Abstract
In this paper we consider the problem of defining rate of occurrence of failures of higher orders for a system whose states form a finite state Markov jump process. Firstly, we derive an explicit formula for evaluating the rate of occurrence of failures of higher order for the system. Secondly, we propose a nonparametric statistical estimator of this function and we discuss its asymptotic properties. The covariance matrix and the asymptotic variance are computed by using the technology of multidimensional matrices. Finally, we provide applications to the modeling of financial credit ratings.
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