Level set Cox processes

Shot Noise Cox Processes

Generalised Shot Noise Cox Processes

We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby a very large class of models for aggregated or clustered point patterns is obtai...

Random tessellations and Cox processes

We consider random tessellations T in R2 and Coxian point processes whose driving measure is concentrated on the edges of T . In particular, we discuss several classes of Poisson-type tessellations which can describe e.g. the infrastructure of telecommunication networks, whereas the Cox processes on their edges can describe the locations of network components. An important quantity associated w...

Palm distributions for log Gaussian Cox processes

This paper establishes a remarkable result regarding Palm distributions for a log Gaussian Cox process: the reduced Palm distribution for a log Gaussian Cox process is itself a log Gaussian Cox process which only differs from the original log Gaussian Cox process in the intensity function. This new result is used to study functional summaries for log Gaussian Cox processes.

Poisson Cox Point Processes for Vehicular Networks

This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks. The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and independent Poisson point processes, conditionally on the Poisson lines, to model vehicles on the roads. We derive basic properties of the point process, in...