Related papers: Means of a Dirichlet process and multiple hypergeo…
In this paper, we study the conditional Dirichlet process (cDP) when a functional of a random distribution is specified. Specifically, we apply the cDP to the functional condition model, a nonparametric model in which a finite-dimensional…
The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…
When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider…
We study a 3-parametric family of stochastic point processes on the one-dimensional lattice originated from a remarkable family of representations of the infinite symmetric group. We prove that the correlation functions of the processes are…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
This paper will demonstrate some new techniques for developing the theory of Asian (arithmetic average) options pricing. We discuss the basic derivation of the diffusion equations, and how various techniques from potential theory can be…
We establish some limit theorems for quasi-arithmetic means of random variables. This class of means contains the arithmetic, geometric and harmonic means. Our feature is that the generators of quasi-arithmetic means are allowed to be…
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…
We develop a Bayesian hierarchical semiparametric model for phenomena related to time series of counts. The main feature of the model is its capability to learn a latent pattern of heterogeneity in the distribution of the process innovation…
Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…
We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…
Random flights in $\mathbb{R}^d,d\geq 2,$ with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position $\underline{\bf X}_d(t),\,t>0,$ when the number of…
We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper…
We present a novel integral representation for the biharmonic Dirichlet problem. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman-Lauricella integral representation…
Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location…
The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is…
The moments of quadratic Dirichlet $L$-functions over function fields have recently attracted much attention with the work of Andrade and Keating. In this article, we establish lower bounds for the mean values of the product of quadratic…
This is a survey of the Deligne-Mostow theory of Lauricella functions, or what almost amounts to the same thing, of the period map for cyclic coverings of the Riemann sphere.
Directional data require specialized probability models because of the non-Euclidean and periodic nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional…
The Laguerre symmetric functions introduced in the note are indexed by arbitrary partitions and depend on two continuous parameters. The top degree homogeneous component of every Laguerre symmetric function coincides with the Schur function…