'Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora'
Abstract
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
