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A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…
New proofs are given of the existence of the compensator (or dual predictable projection) of a locally integrable c\'adl\'ag adapted process of finite variation and of the existence of the quadratic variation process for a c\'adl\'ag local…
Determinantal process is a dynamical extension of a determinantal point process such that any spatio-temporal correlation function is given by a determinant specified by a single continuous function called the correlation kernel.…
Consider a symmetrical conflict relationship between the points of a point process. The Mat\'ern type constructions provide a generic way of selecting a subset of this point process which is conflict-free. The simplest one consists in…
When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…
Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…
When the \textit{martingale representation property} holds, we call any local martingale which realizes the representation a \textit{representation process}. There are two properties of the \textit{representation process} which can greatly…
We consider a family {P} of determinantal point processes arising in representation theory and random matrix theory. The processes live on the one-dimensional lattice and their correlation kernels correspond to projection operators in the…
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees).…
Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…
Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern datasets where nearby points repel each other. Such…
Fragmentation processes are part of a broad class of models describing the evolution of a system of particles which split apart at random. These models are widely used in biology, materials science and nuclear physics, and their asymptotic…
Fitting models for non-Poisson point processes is complicated by the lack of tractable models for much of the data. By using large samples of independent and identically distributed realizations and statistical learning, it is possible to…
We introduce and study a multiparameter Poisson process (MPP). In a particular case, it is observed that the MPP has a unique representation. Its subordination with the multivariate subordinator and inverse subordinator are studied in…
Assume that several competing methods are available to estimate a parameter in a given statistical model. The aim of estimator averaging is to provide a new estimator, built as a linear combination of the initial estimators, that achieves…
Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose…
In contrast to the usual procedure of estimating the distribution of a time series and then obtaining the quantile from the distribution, we develop a compensatory model to improve the quantile estimation under a given distribution…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…