相关论文: On Layered Stable Processes

Layered control is essential for managing complexity in large-scale systems, employing progressively coarser models at higher layers. While significant advances have been made for fully observable systems, the theoretical foundations of…

This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…

Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…

Graphs are now ubiquitous in almost every field of research. Recently, new research areas devoted to the analysis of graphs and data associated to their vertices have emerged. Focusing on dynamical processes, we propose a fast, robust and…

This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…

We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…

Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and…

Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…

We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…

In this paper, we begin our discussion with some of the well-known methods available in the literature for the estimation of the parameters of a univariate/multivariate stable distribution. Based on the available methods, a new hybrid…

The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…

This paper introduces a mathematical framework of a stochastic process model as a generalization of diffusion stochastic processes to model latent variables in categorical responses given unobserved random effects and maximum likelihood…

Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…