We provide Monte Carlo estimators for the derivatives of functionals of Poisson-driven systems, and apply the theoretical results to models of interest in stochastic geometry and insurance

We provide a large deviation principle for the interference in a simple model of wireless communication

We derive the pair correlation function of spatial Hawkes processes and discuss its connections with the Bartlett spectrum and other summary statistics.

For a risk process with reserve dependent premium rate, we study sample path large deviations and provide a fast simulation procedure to estimate the corresponding ruin probability.

We prove scalar and sample path large deviations principles for Poisson cluster processes and apply the results to Hawkes processes.

We consider a class of risk processes with delayed claims, and we provide ruin probability estimates under large claim assumptions

We provide sample path large deviation principles for Poisson shot noise processes, and applicatons in queueing theory

We consider risk processes with delay in a Markovian environment and study the asymptotic behavior of finite and infinite horizon ruin probabilities

We propose a stochastic algorithm for solving NP-hard combinatorial optimization problems and study its convergence

We introduce a new class of models for aggregate or clustered point patterns, which encompasses and extends most of the classical models. We derive summary statistics and simulation procedures.

We study the asymptotic behavior of risk processes perturbed by a diffusion, Cox arrivals and delayed claims

Using importance sampling we give an asymptotic efficient simulation law for risk processes with delayed claims

In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and non trivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

In this paper we obtain the rate of convergence to equilibrium of a class of interacting marked point processes, introduced by Kerstan, in two different situations. Indeed, we prove the exponential and subexponential ergodicity of such a class of stochastic processes. Our results are an extension of the corresponding results in a paper by Bremaud, Nappo and Torrisi (JAP, 2002). The generality of the dynamics which we take into account allows the application to the so-called loss networks, and multivariate birth-and-death processes.

We consider a simple exchangeable model, which accounts for heterogeneity and dependence. Based on this model, we show how, and in which sense, situations of negative aging arise in a natural way from conditions of heterogeneity among items.