Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework

Strong convergence of a class of non-homogeneous Markov arrival processes to a Poisson process

In this paper, we are concerned with a time-inhomogeneous version of the Markovian Arrival Process. Under the assumption that the environment process is asymptotically time-homogeneous, we discuss a Poisson approximation of the counting process of arrivals when the arrivals are rare. We provide a rate of convergence for the distance in variation. Poisson-type approximation for the process resul...

Strong convergence of a class of non-homogeneous Markov Arrivals Processes to a Poisson process

In this paper, we are concerned with a time-inhomogeneous version of the Markovian Arrival Process. Under the assumption that the environment process is asymptotically time-homogeneous, we discuss a Poisson approximation of the counting process of arrivals when the arrivals are rare. We provide a rate of convergence for the distance in variation. Poisson-type approximation for the process resul...

Numerical Solution of Non-Homogeneous Markov Processes through Uniformization

Numerical algorithms based on uniformization have been proven to be numerically stable and computationally at tractive to compute transient state distributions in ho mogeneous continuous time Markov chains Recently Van Dijk van Dijk formulated uniformization for non homogeneous Markov processes and it is of interest to investigate numerical algorithms based on uniformiza tion for non homogeneou...

Estimating the parameters of a seasonal Markov-modulated Poisson process

On Double Periodic Non–Homogeneous Poisson Processes

Non-homogenous Poisson processes with periodic claim intensity rate are proposed as the claim counting process of risk theory. We introduce a doubly periodic Poisson model with short and long term trends, illustrated by a double-beta intensity function. Here periodicity does not repeat the exact same short term pattern every year, but lets its peak intensity vary over a longer period. This mode...