Related papers: A copula-based method to build diffusion models wi…
Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and…
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences…
Copulas are a fundamental tool for modelling multivariate dependencies in data, forming the method of choice in diverse fields and applications. However, the adoption of existing models for multimodal and high-dimensional dependencies is…
We are studying the problems of modeling and inference for multivariate count time series data with Poisson marginals. The focus is on linear and log-linear models. For studying the properties of such processes we develop a novel conceptual…
Probability density estimation from observed data constitutes a central task in statistics. In this brief, we focus on the problem of estimating the copula density associated to any observed data, as it fully describes the dependence…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…
The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2011) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…
We study a diffusion process with random space-time dependent coefficients. Moreover the diffusion matrix is allowed to degenerate. An invariance principle is proved provided that the diffusion coefficient is controlled by a time…
Discrete diffusion models have recently shown significant progress in modeling complex data, such as natural languages and DNA sequences. However, unlike diffusion models for continuous data, which can generate high-quality samples in just…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum…
Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged…
We consider multivariate copula-based stationary time-series under Gaussian subordination. Observed time series are subordinated to long-range dependent Gaussian processes and characterized by arbitrary marginal copula distributions. First…
We propose to construct copulas from the inversion of nonlinear state space models. These allow for new time series models that have the same serial dependence structure of a state space model, but with an arbitrary marginal distribution,…
Modelling multivariate circular time series is considered. The cross-sectional and serial dependence is described by circulas, which are analogs of copulas for circular distributions. In order to obtain a simple expression of the dependence…
Copulas are popular as models for multivariate dependence because they allow the marginal densities and the joint dependence to be modeled separately. However, they usually require that the transformation from uniform marginals to the…
This paper addresses the problem of quantification and propagation of uncertainties associated with dependence modeling when data for characterizing probability models are limited. Practically, the system inputs are often assumed to be…
We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle…