Related papers: Conditional Intensity and Gibbsianness of Determin…
We construct marked Gibbs point processes in $\mathbb{R}^d$ under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…
We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…
Noncolliding Brownian motion (Dyson's Brownian motion model with parameter $\beta=2$) and noncolliding Bessel processes are determinantal processes; that is, their space-time correlation functions are represented by determinants. Under a…
In this paper, we study a class of self-exciting point processes. The intensity of the point process has a nonlinear dependence on the past history and time. When a new jump occurs, the intensity increases and we expect more jumps to come.…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…
We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…
We study first-order phase transitions in continuum Gibbs point processes with saturated interactions. These interactions form a broad class of Hamiltonians in which the local energy in regions of high particle density depends only on the…
We consider a new type of lookdown processes where spatial motion of each individual is influenced by an individual noise and a common noise, which could be regarded as an environment. Then a class of probability measure-valued processes on…
The main result of this paper is that conditional measures of generalized Ginibre point processes, with respect to the configuration in the complement of a bounded open subset on $\mathbb{C}$, are orthogonal polynomial ensembles with…
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.…
We introduce and study a class of determinantal probability measures generalising the class of discrete determinantal point processes. These measures live on the Grassmannian of a real, complex, or quaternionic inner product space that is…
We consider mixture models where location parameters are a priori encouraged to be well separated. We explore a class of determinantal point process (DPP) mixture models, which provide the desired notion of separation or repulsion. Instead…
The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed…
Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data…
We propose a novel continuous testing framework to test the intensities of Poisson Processes. This framework allows a rigorous definition of the complete testing procedure, from an infinite number of hypothesis to joint error rates. Our…
Lower bounds for persistence probabilities of stationary Gaussian processes in discrete time are obtained under various conditions on the spectral measure of the process. Examples are given to show that the persistence probability can decay…
This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for…