Related papers: On multivariate modifications of Cramer Lundberg r…

We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…

We consider together the retrospective and the sequential change-point detection in a general class of integer-valued time series. The conditional mean of the process depends on a parameter $\theta^*$ which may change over time. We propose…

This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under…

We consider two bivariate models with two-way interactions in context of risk and queueing theory. The two entities interact with each other by providing assistance but otherwise evolve independently. We focus on certain random quantities…

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…

In this paper, we consider a simple test case of multiparameter product systems that arise out of random measures. We associate a product system to a stationary Poisson process and a stationary compound Poisson process. We show that the…

For a general free L\'evy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the L\'evy-It\^o representation of the original process. For a general free compound…

The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…

The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral…

Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

This paper discusses infill asymptotics for logistic regression estimators for spatio-temporal point processes whose intensity functions are of log-linear form. We establish strong consistency and asymptotic normality for the parameters of…

A number of numeric approaches to simulate Poisson point processes with arbitrary event rates are presented and implemented for R. They include the simulation of the number of points and their location as well as the determination of…

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…

This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and…

We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing ad hoc approach, such as the last value carried forward, is biased. We propose a…

We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains…

Asymptotic properties, both consistency and weak convergence, of estimators arising in a general class of dynamic recurrent event models are presented. The class of models take into account the impact of interventions after each event…

This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common…

We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…

Motivated by applications in cybersecurity and epidemiology, we consider the problem of detecting an abrupt change in the intensity of a Poisson process, characterised by a jump (non transitory change) or a bump (transitory change) from…