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This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical…
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…
Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of…
A mixed Gaussian fractional process $\{Y(t)\}_{t \in {\Bbb R}} = \{PX(t)\}_{t \in {\Bbb R}}$ is a multivariate stochastic process obtained by pre-multiplying a vector of independent, Gaussian fractional process entries $X$ by a nonsingular…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains…
The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance…
Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the…
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…
This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…
We are interested in estimating the location of what we call "smooth change-point" from $n$ independent observations of an inhomogeneous Poisson process. The smooth change-point is a transition of the intensity function of the process from…
We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible…
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…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
A parametric point process model is developed, with modeling based on the assumption that sequential observations often share latent phenomena, while also possessing idiosyncratic effects. An alternating optimization method is proposed to…
We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $t\to -\infty$ to asymptotic dynamics as $t\to +\infty$. The main novelty is the construction of modified…
High-dimensional self-exciting point processes have been widely used in many application areas to model discrete event data in which past and current events affect the likelihood of future events. In this paper, we are concerned with…