相关论文: Study on discrete degenerate Bell distributions wi…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…

This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to…

Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated…

When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…

In this paper, we propose a novel robust stochastic optimization approach with a distinctive consideration for rare events, in which divergence measures are used to bound the event-wise ambiguity sets. This is done by using the Poisson…

A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed…

We consider a fractional counting process with jumps of amplitude $1,2,\ldots,k$, with $k\in \mathbb{N}$, whose probabilities satisfy a suitable system of fractional difference-differential equations. We obtain the moment generating…

Randomness is a fundamental feature in nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize…

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…

The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates…

This paper considers the distributionally robust chance constrained Markov decision process with random reward and ambiguous reward distribution. We consider individual and joint chance constraint cases with Kullback-Leibler divergence…

In this article, we study a non-uniform distribution on permutations biased by their number of records that we call \emph{record-biased permutations}. We give several generative processes for record-biased permutations, explaining also how…

We obtain explicit bounds on the truncation error of the cumulant series of a bounded complex function of a random vector with independent components. The bounds are based on multidimensional differences. This extends the theory of the…

A class of random recursive sequences (Y_n) with slowly varying variances as arising for parameters of random trees or recursive algorithms leads after normalizations to degenerate limit equations of the form X\stackrel{L}{=}X. For…

In 2003 Klazar proved that the ordinary generating function of the sequence of Bell numbers is differentially transcendental over the field $\mathbb{C}(\{t\})$ of meromorphic functions at $0$. We show that Klazar's result is an instance of…

We consider the infinite divisibility of distributions of some well-known inverse subordinators. Using a tail probability bound, we establish that distributions of many of the inverse subordinators used in the literature are not infinitely…

Real count data time series often show the phenomenon of the underdispersion and overdispersion. In this paper, we develop two extensions of the first-order integer-valued autoregressive process with Poisson innovations, based on binomial…

A new multivariate integer-valued Generalized AutoRegressive Conditional Heteroscedastic process based on a multivariate Poisson generalized inverse Gaussian distribution is proposed. The estimation of parameters of the proposed…

We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…

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,…