Abstract We consider a Lévy process Y ( t ) that is not continuously observed, but rather inspected at Poisson( $\omega$ moments only, over an exponentially distributed time $T_\beta$ with parameter $\beta$ . The focus lies on the analysis of distribution running maximum such inspection up to , denoted by $Y_{\beta,\omega}$ Our main result decomposition: we derive remarkable distributional equa...

We have developed a method for quantifying neural response changes in terms of the Kullback-Leibler distance between the intensity functions for each stimulus condition. We use empirical histogram estimates to characterize the intensity function of the neural response. A critical factor in determining the histogram estimates is selection of binwidth. In this work we analytically derive the Kull...

Prediction of events such as part replacement and failure plays a critical role in reliability engineering. Event stream data are commonly observed manufacturing teleservice systems. Designing predictive models for individual units based on event streams is challenging an underexplored problem. In this work, we propose nonparametric prognostic framework individualized prediction the inhomogeneo...

Abstract Consider two independent Poisson point processes of unit intensity in the Euclidean space dimension d at least 3. We construct a perfect matching between sets that is factor (i.e., measurable function configurations commutes with translations), and property distance matched configuration points has tail distribution decays as fast possible magnitude, namely, $$b\exp (-cr^d)$$ <mml:math...