On stationary stochastic flows and palm probabilities of surface processes
成果类型：
Article
署名作者：
Last, G; Schassberger, R
署名单位：
Braunschweig University of Technology
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
2000
页码：
463-492
关键词：
摘要：
We consider a random surface Phi in R-d tessellating the space into cells and a random vector held u which is smooth on each cell but may jump on Phi. Assuming the pair (Phi, u) stationary we prove a relationship between the stationary probability measure P and the Palm probability measure P-Phi, of P with respect to the random surface measure associated with Phi. This result involves the flow of u induced on the individual cells and generalizes a well-known inversion formula for stationary point processes on the line. An immediate consequence of this result is a formula for certain generalized contact distribution functions of Phi, and as first application we prove a result on the spherical contact distribution in stochastic geometry. As another application we prove an invariance property for P-Phi which again generalizes a corresponding property in dimension d = 1. Under the assumption that the flow can be defined for all time points, we consider the point process N of sucessive crossing times starting in the origin 0. If the flow is volume preserving then N is stationary and we express its Palm probability in terms of P-Phi.