Strong consistency of Kernel density estimates for Markov chains failure rates

Abstract

For a homogeneous and uniformly ergodic Markov chain, with transition kernel \(P(x, A) = \int_{A} f(y|x)\hbox{d}y, x \in E \subset R^{d}\), we analyse some reliability measures and failure rates associated with the transition probabilities. Sufficient conditions for strong consistency are obtained for estimates based on kernel density estimators.