相关论文: Differentiating sigma-fields for Gaussian and shif…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…

This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…

The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic…

We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds…

We establish diffusion and fractional Brownian motion approximations for motions in a Markovian Gaussian random field with a nonzero mean.

We introduce a new class of self-similar Gaussian stochastic processes, where the covariance is defined in terms of a fractional Brownian motion and another Gaussian process. A special case is the solution in time to the fractional-colored…

Recently, Hammond and Sheffield introduced a model of correlated random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension $d\geq 2$. We…

We aim to link random fields and marked point processes and therefore introduce a new class of stochastic processes which are defined on a random set in R^d. Unlike for random fields, the mark covariance function of a marked random set is…

We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle--Mat\'ern fields, are defined via a fractional stochastic differential equation on the compact metric…

Massive and massless Gaussian free fields can be described as generalized Gaussian processes indexed by an appropriate space of functions. In this article we study various approaches to approximate these fields and look at the fractal…

We study fundamental properties of the gamma process and their relation to various topics such as Poisson-Dirichlet measures and stable processes. We prove the quasi-invariance of the gamma process with respect to a large group of linear…

We present new properties for the Fractional Poisson process and the Fractional Poisson field on the plane. A martingale characterization for Fractional Poisson processes is given. We extend this result to Fractional Poisson fields,…

We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the…

We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…

We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…

We consider a general class of integro-differential evolution equations which includes the governing equation of the generalized grey Brownian motion and the time- and space-fractional heat equation. We present a general relation between…

This primer explains how continuous-time stochastic processes (precisely, Brownian motion and other Ito diffusions) can be defined and studied on manifolds. No knowledge is assumed of either differential geometry or continuous-time…

High-dimensional classification and feature selection tasks are ubiquitous with the recent advancement in data acquisition technology. In several application areas such as biology, genomics and proteomics, the data are often functional in…

For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…