Gamma distributions for stationary Poisson flat processes

Poisson processes (and mixture distributions)

Stationary Distributions for Jump Processes with Memory

We analyze a jump processes Z with a jump measure determined by a “memory” process S. The state space of (Z, S) is the Cartesian product of the unit circle and the real line. We prove that the stationary distribution of (Z, S) is the product of the uniform probability measure and a Gaussian distribution.

Quasi-stationary distributions for Lévy processes

In recent years there has been some focus on the behaviour of one dimensional Lévy processes and random walks conditioned to stay positive; see for example Bertoin (1993, 1996), Bertoin and Doney (1994), Chaumont (1996) and Chaumont and Doney (2004). The resulting conditioned process is transient. In older literature however, one encounters for special classes of random walks and Lévy processes...

Quasi-stationary distributions for population processes

Key-words: population dynamics, quasi-stationarity, Yaglom’s limit, birth and death process, logistic Feller diffusion.

Segmentation algorithm for non-stationary compound Poisson processes

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of a time series. The process is composed of consecutive patches of variable length. In each patch the process is described by a stationary compound Poisson process, i.e. a Poisson process where each cou...