Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel me...

We consider an M/G/1 queue with the following form of customer impatience: an arriving customer balks or reneges when its virtual waiting time, i.e., the amount of work seen upon arrival, is larger than a certain random patience time. We consider the number of customers in the system, the maximum workload during a busy period, and the length of a busy period. We also briefly treat the analogous...

Abstract This work shows how interaction is essential for storytelling with a child. A corpus of narrative dialogues between parents and their children was coded with a mentalist grid. The results of two modelling methods were analysed by an expert in parent-child dialogue analysis. The extraction of dialogue patterns reveals regularities explaining the character’s emotion. Results showed that ...