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We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has…

Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…

We study a linear-fractional Bienaym\'e-Galton-Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads…

Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…

The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science, and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but not identically distributed…

Recently the so-called Prabhakar generalization of the fractional Poisson counting process attracted much interest for his flexibility to adapt real world situations. In this renewal process the waiting times between events are IID…

A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…

We consider a Gaussian Volterra process with compound Poisson jumps and derive its prediction law.

Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…

With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…

A new family of fractional counting processes based on a three-parameter generalized Mittag-Leffler function was introduced and studied. As applications we develop a fractional generalized compound process, introduce and develop fractional…

In this paper, we introduce a generalized birth process (GBP) which performs jumps of size $1,2,\dots,k$ whose rates depend on the state of the process at time $t\geq0$. We derive a non-exploding condition for it. The system of differential…

Neural Processes (NPs) are a family of conditional generative models that are able to model a distribution over functions, in a way that allows them to perform predictions at test time conditioned on a number of context points. A recent…

We review the experimental as well as the phenomenology status of Generalized Parton Distributions (GPDs), focusing on recent data on Deeply Virtual Compton Scattering and Deep Virtual Meson Production. We also describe the various…

We establish sample-path large deviation principles for the centered cumulative functional of marked Poisson cluster processes in the Skorokhod space equipped with the M1 topology, under joint regular variation assumptions on the marks and…

In this paper, we introduce drifted versions of the generalized counting process (GCP) with a deterministic drift and a random drift. The composition of stable subordinator with an independent inverse stable subordinator is taken as the…

The Poisson process, especially the nonhomogeneous Poisson process (NHPP), is an essentially important counting process with numerous real-world applications. Up to date, almost all works in the literature have been on the estimation of…

Data of the form of event times arise in various applications. A simple model for such data is a non-homogeneous Poisson process (NHPP) which is specified by a rate function that depends on time. We consider the problem of having access to…

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…

We study the process of suitably normalized successive return times to rare events in the setting of infinite-measure preserving dynamical systems. Specifically, we consider small neighborhoods of points whose measure tends to zero. We…