Copulas and Markov processes

ON THE INFINITE ORDER MARKOV PROCESSES

The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.

Multivariate Counting Processes: Copulas and beyond By

Multivariate stochastic processes with Poisson marginals are of interest in insurance and finance; they can be used to model the joint behaviour of several claim arrival processes, for example. We discuss various methods for the construction of such models, with particular emphasis on the use of copulas. An important class of multivariate counting processes with Poisson marginals arises if the ...

Copulas selection in pairwise Markov chain

The Hidden Markov Chain (HMC) model considers that the process of unobservable states is a Markov chain. The Pairwise Markov Chain (PMC) model however considers the couple of processes of observations and states as a Markov chain. It has been shown that the PMC model is strictly more general than the HMC one, but retains the ease of processings that made the success of HMC in a number of applic...

The KTH Visit in Semi-Markov Processes

Unsupervised Signal Restoration Using Copulas and Pairwise Markov Chains

This work deals with the statistical restoration of hidden discrete signals. The problem we deal with is how to take into account, in recent pairwise and triplet Markov chain context, complex noises that can be non-Gaussian, correlated, and of class-varying nature. We propose to solve this modeling problem using Copulas. The interest of the new modeling is validated by experiments performed in ...