Related papers: Some Diffusion Processes Associated With Two Param…

We introduce Pairwise Distance-Diffusion Analysis (PDDA), a geometric framework for estimating the Hurst exponent from distance plots of long-memory stochastic processes. A single construction yields two complementary routes: R/S-PDDA, a…

We present and analyze a discontinuous Petrov-Galerkin method with optimal test functions for a reaction-dominated diffusion problem in two and three space dimensions. We start with an ultra-weak formulation that comprises parameters…

We construct the entropic measure $\mathbb{P}^\beta$ on compact manifolds of any dimension. It is defined as the push forward of the Dirichlet process (another random probability measure, well-known to exist on spaces of any dimension)…

We introduce a new approach to absolute continuity of laws of Poisson functionals. It is based on the {\it energy image density} property for Dirichlet forms and on what we call {\it the lent particle method} which consists in adding a…

We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between…

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 $visual$…

We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using non-symmetric Dirichlet forms and their convergence in a sense close to the Mosco-convergence, we…

This article provides tools for the study of the Dirichlet random walk in $\mathbb{R}^d$. By this we mean the random variable $W=X_1\Theta_1+\cdots+X_n\Theta_n$ where $X=(X_1,\ldots,X_n) \sim \mathcal{D}(q_1,\ldots,q_n)$ is Dirichlet…

We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…

A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…

The hierarchical Dirichlet process is a discrete random measure used as a prior in Bayesian nonparametrics and motivated by the study of groups of clustered data. We study the asymptotic behavior of the power sum symmetric polynomials for…

We study the shrinking Pearson random walk in two dimensions and greater, in which the direction of the Nth is random and its length equals lambda^{N-1}, with lambda<1. As lambda increases past a critical value lambda_c, the endpoint…

In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…

We investigate the dynamics of a kicked particle in an infinite square well undergoing frequent measurements of energy. For a large class of periodic kicking force, constant diffusion is found in such a non-KAM system. The influence of…

Palm distributions are critical in the study of point processes. In the present paper we focus on a point process $\Phi$ defined as the superposition, i.e., sum, of two independent point processes, say $\Phi = \Phi_1 + \Phi_2$, and we…

We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The…

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…

We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation $\pi \in \mathbb{S}_n$ is proportional to $q^{\textrm{inv}(\pi)}$ where $0<q\le 1$ and…

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…

The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical…