Related papers: Modelling Levy space-time white noises

This paper introduces a geometric method for proving ergodicity of degenerate noise driven stochastic processes. The driving noise is assumed to be an arbitrary Levy process with non-degenerate diffusion component (but that may be applied…

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…

Let $\mu$ be a probability measure (or corresponding random variable) such that all moments $\mu_n$ exist. Knowledge of the moments is not sufficient to determine infinite divisibility of the measure; we show also that infinitely divisible,…

Normalized random measures with independent increments represent a large class of Bayesian nonaprametric priors and are widely used in the Bayesian nonparametric framework. In this paper, we provide the posterior consistency analysis for…

Semi-Levy process is an additive process with periodically stationary increments. In particular, it is a generalization of Levy process. The dichotomy of recurrence and transience of Levy processes is well known, but this is not necessarily…

This paper provides a construction of an uncountable family of i.i.d. random vectors, indexed by the points of a nonatomic measure space, such that (a) a sample is a measurable function from the index space, and (b) an idealization of the…

We address the problem of recognizing alpha-stable Levy distribution with Levy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the…

Despite recent monumental advances in the field, many Natural Language Processing (NLP) models still struggle to perform adequately on noisy domains. We propose a novel probabilistic embedding-level method to improve the robustness of NLP…

In the context of non-Gaussian analysis, Schneider [27] introduced grey noise measures, built upon Mittag-Leffler functions; analogously, grey Brownian motion and its generalizations were constructed (see, for example, [25], [6], [7], [8]).…

We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational…

We propose a simple model based on the Gnedenko limit theorem for simulation and studies of the ordinary Levy motion, that is, a random process, whose increments are independent and distributed with a stable probability law. We use the…

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…

We present two linear relations between an arbitrary (real tempered second order) generalized stochastic process over $\mathbb{R}^{d}$ and White Noise processes over $\mathbb{R}^{d}$. The first is that any generalized stochastic process can…

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the…

Complex dynamical systems which are governed by anomalous diffusion often can be described by Langevin equations driven by L\'evy stable noise. In this article we generalize nonlinear stochastic differential equations driven by Gaussian…

In this paper we introduce a new class of state space models based on shot-noise simulation representations of non-Gaussian L\'evy-driven linear systems, represented as stochastic differential equations. In particular a conditionally…

We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to L\'evy-type processes…

Inferring the causal structure of a set of random variables from a finite sample of the joint distribution is an important problem in science. Recently, methods using additive noise models have been suggested to approach the case of…

Social science research often hinges on the relationship between categorical variables and outcomes. We introduce CAVIAR, a novel method for embedding categorical variables that assume values in a high-dimensional ambient space but are…

Label noise - incorrect labels assigned to observations - can substantially degrade the performance of supervised classifiers. This paper proposes a label noise cleaning method based on Bernoulli random sampling. We show that the mean label…