A joint renewal process used to model event based data

Model Renewal processes have been a frequent object of analysis in early studies of stochastic processes, see Cox (1962), for instance. Only recently the idea of parallel renewal processes receives more attention, see Borgelt and Picado-Muino (2012), Gaigalas (2003), Kai et al. (2014), CRC (1994), Kallen et al. (2010), Truccolo (2005), Modir et al. (2010). However, little emphasis has been given to the subject of stochastic dependence between processes so far, with few exceptions such as shown in Borgelt and Picado-Muino (2012) or Truccolo (2005), Modir et al. (2010). Spike train analysis is an active neurobiological research area calling for parallel renewal processes. The latter paper emphasizes stochastic dependence between point processes described by conditionally independent intensity functions. In the same spirit, stochastic dependence between events will be at the core of the present paper in combination with a linear damage model in a condition Abstract