Generalised Shot Noise Cox Processes

Properties of Spatial Cox Process Models

Probabilistic properties of Cox processes of relevance for statistical modeling and inference are studied. Particularly, we study the most important classes of Cox processes, including log Gaussian Cox processes, shot noise Cox processes, and permanent Cox processes. We consider moment properties and point process operations such as thinning, displacements, and superpositioning. We also discuss...

A note on bounds and monotonicity of spatial stationary Cox shot noises

We consider shot-noise processes and max-shot-noise processes driven by spatial stationary Cox (doubly stochastic Poisson) processes. We derive the upper and lower bounds of them in terms of the increasing convex order, which is known as the order relation to compare the variability of random variables. Furthermore, under some regularity assumption of the random intensity fields of Cox processe...

Shot Noise Cox Processes

Ruin Probabilities for Risk Processes with Non-stationary Arrivals and Subexponential Claims

In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and nonrenewal. We give three examples of non-stationary and non-renewal point processes: Hawkes proces...

Ruin Probabilities and Aggregrate Claims Distributions for Shot Noise Cox Processes

We consider a risk process Rt where the claim arrival process is a superposition of a homogeneous Poisson process and a Cox process with a Poisson shot noise intensity process, capturing the effect of sudden increases of the claim intensity due to external events. The distribution of the aggregate claim size is investigated under these assumptions. For both light-tailed and heavy-tailed claim s...