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The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
Inspired by R. Speicher's multidimensional free central limit theorem and semicircle families, we prove an infinite dimensional compound Poisson limit theorem in free probability, and define infinite dimensional compound free Poisson…
Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…
Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…
The dynamics of a freely diffusing particle in a two-dimensional channel with cross sectional area $A(x)$, can be effectively described by a one-dimensional diffusion equation under the action of a potential of mean force $U(x)=-k_BT\ln…
The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation of fractional diffusion processes. Here we have analyzed…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
We consider a generalization of spatial branching coalescing processes in which the behaviour of individuals is not (necessarily) independent, on the contrary, individuals tend to take simultaneous actions. We show that these processes have…
In the Hammersley-Aldous-Diaconis process infinitely many particles sit in R and at most one particle is allowed at each position. A particle at x$ whose nearest neighbor to the right is at y, jumps at rate y-x to a position uniformly…
Random discrete distributions, say $F,$ known as species sampling models, represent a rich class of models for classification and clustering, in Bayesian statistics and machine learning. They also arise in various areas of probability and…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Although its probability mass function (pmf) is known, what is lacking is a $visual$…
Ferguson's Dirichlet process plays an important role in nonparametric Bayesian inference. Let $P_a$ be the Dirichlet process in $\mathbb{R}$ with a base probability measure $H$ and a concentration parameter $a>0.$ In this paper, we show…
In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape…
The present paper originated from our previous study of the problem of harmonic analysis on the infinite symmetric group. This problem leads to a family {P_z} of probability measures, the z-measures, which depend on the complex parameter z.…
We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the moment, imagine you run two Brownian-like particles on the…
We propose in this paper a construction of a diffusion process on the Wasserstein space P\_2(R) of probability measures with a second-order moment. This process was introduced in several papers by Konarovskyi (see e.g. "A system of…
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…
We extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of time-dependent…