Ergodicity Conditions and Cesaro Limit Results for Marked Point Processes

In Palm theory it is very common to consider several distributions to describe the characteristics of the system.To study a stationary marked point process, the time-stationary distribution P and its event-stationary Palm distributions P 0 L with respect to sets L of marks can all be used as starting point.When P is used, a modi ed, event-stationary version Q 0 L of P 0 L is de ned as the limit of an obvious discrete-time Ces aro average.In a sense this modi ed Palm distribution is more natural than the ordinary one.When a Palm distribution P 0 L 0 is taken as starting point, we can approximate another modi ed, event-stationary version of P 0 L by considering discrete-time Ces aro averages and a modi ed, time-stationary version QL of P by considering continuous-time Ces aro averages.These and other limit results are corollaries of uniform limit theorems for Ces aro averaged functionals.In essence, this paper presents a profound study of the relationship between P; P 0 L ; P 0 L 0, and modi ed versions of them, and their connections with ergodicity conditions and long-run averages of Ces aro type.