We prove that arbitrary Hunt processes on a general state space can be approximated by multivariate Poisson processes starting from each point of the state space. The key point is that no additional regularity assumption on the state space and on the underlying transition semigroup is used.

In this paper we provide theoretical support for the so-called “Sigmoidal Gaussian Cox Process” approach to learning the intensity of an inhomogeneous Poisson process on a ddimensional domain. This method was proposed by Adams, Murray and MacKay (ICML, 2009), who developed a tractable computational approach and showed in simulation and real data experiments that it can work quite satisfactorily...

The theory of sparse stochastic processes offers a broad class of statistical models to study signals. In this framework, signals are represented as realizations of random processes that are solution of linear stochastic differential equations driven by white Lévy noises. Among these processes, generalized Poisson processes based on compoundPoisson noises admit an interpretation as random L-spl...

We present a method for constructing dependent Dirichlet processes. The new approach exploits the intrinsic relationship between Dirichlet and Poisson processes in order to create a Markov chain of Dirichlet processes suitable for use as a prior over evolving mixture models. The method allows for the creation, removal, and location variation of component models over time while maintaining the p...

Superposition is a mapping on point configurations that sends the n-tuple (x1, . . . , xn) ∈ X into the n-point configuration {x1, . . . , xn} ⊂ X , counted with multiplicity. It is an additive set operation such the superposition of a k-point configuration in X is a kn-point configuration in X . A Poisson superposition process is the superposition in X of a Poisson process in the space of fini...

We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet process mixtures for this density, combined with nonparametric or semiparametric modeling for the mark distribution, yield flexible prior models for the mar...