In this paper, we provide a method for modelling stationary time series. We allow the family of marginal densities for the observations to be speci ed. Our approach is to construct the model with a speci ed marginal family and build the dependence structure around it. We show that the resulting time series is linear with a simple autocorrelation structure. In particular, we present an original ...

Mathematical modelling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact master equations of the propagation process are derived for an arbitrary hypergraph given by its incidence matrix. Based on these, moment closure approxima...

We characterize joint tails and tail dependence for a class of stochastic volatility processes. We derive the exact joint tail shape of multivariate stochastic volatility with innovations that have a regularly varying distribution tail. This is used to give four new characterizations of tail dependence. In three cases tail dependence is a non-trivial function of linear volatility memory paramet...

We characterize joint tails and tail dependence for a class of stochastic volatility processes. We derive the exact joint tail shape of multivariate stochastic volatility with innovations that have a regularly varying distribution tail. This is used to give four new characterizations of tail dependence. In three cases tail dependence is a non-trivial function of linear volatility memory paramet...

For each n ≥ 1, let {Xj,n}1≤j≤n be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions for the convergence in distribution of the point process Nn = ∑n j=1 δXj,n to an infinitely divisible point process. From the point process convergence, we obtain the convergence in distribution of the partial sum sequence Sn = ∑n j=1 Xj,n to...

This paper gathers recent results in the analysis of multivariate extreme values and illustrates their actuarial application. We review basic and essential background on univariate extreme value theory and stochastic dependence and then provide an introduction to multivariate extreme value theory. We present important concepts for the analysis of multivariate extreme values and collect research...

In a large-scale production system such as building a Boeing 777 airplane, there are more than ten thousand jobs. The interdependence structure among jobs and some jobs’ delay’s influence on the other jobs in different manufacturing areas are critical information to understand the status of their area. Relationship among groups of jobs may help us find the root cause of problems, to estimate re...