Absolute regularity and Brillinger-mixing of stationary point processes

作者：Heinrich Lothar^*; Pawlas Zbynek

来源：Lithuanian Mathematical Journal, 2013, 53(3): 293-310.

DOI：10.1007/s10986-013-9209-5

• Palm distribution
• (reduced) factorial cumulant measure
• Brillinger-mixing
• higher-order covariance measure
• beta-mixing coefficient
• germ-grain model
• dependently thinned point process

We study the following problem: How to verify Brillinger-mixing of stationary point processes in by imposing conditions on a suitable mixing coefficient? For this, we define an absolute regularity (or beta-mixing) coefficient for point processes and derive, in terms of this coefficient, an explicit condition that implies finite total variation of the kth-order reduced factorial cumulant measure of the point process for fixed . To prove this, we introduce higher-order covariance measures and use Statuleviius%26apos; representation formula for mixed cumulants in case of random (counting) measures. To illustrate our results, we consider some Brillinger-mixing point processes occurring in stochastic geometry.

• 出版日期2013-7