Related papers: Stochastic Mappings and Random Distribution Fields…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
A discrete spatial lattice can be cast as a network structure over which spatially-correlated outcomes are observed. A second network structure may also capture similarities among measured features, when such information is available.…
In this work we introduce a theory of stochastic integration for operator-valued integrands with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces. The integral is constructed via the radonification of…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
We describe Stochastic Loewner Evolution on arbitrary Riemann surfaces with boundary using Conformal Field Theory methods. We propose in particular a CFT construction for a probability measure on (clouded) paths, and check it against known…
Multivariate spatial modeling is key to understanding the behavior of materials downstream in a mining operation. The ore recovery depends on the mineralogical composition, which needs to be properly captured by the model to allow for good…
Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In a companion article, we introduced the notion of multiscale (first-order) functional inequalities, which extend standard functional inequalities like…
We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and a trust-region…
We consider the simple hypothesis of letting quantum systems have an inherent random nature. Using well-known stochastic methods we thus derive a stochastic evolution operator which let us define a stochastic density operator whose…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…
We consider Gaussian measures $\mu, \tilde{\mu}$ on a separable Hilbert space, with fractional-order covariance operators $A^{-2\beta}$ resp. $\tilde{A}^{-2\tilde{\beta}}$, and derive necessary and sufficient conditions on $A, \tilde{A}$…
We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the…
In this work we investigate the multivariate statistical description of the matter distribution in the nonlinear regime. We introduce the multivariate Edgeworth expansion of the lognormal distribution to model the cosmological matter field.…
A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…
The paper addresses the question whether a random functional, a map from a set $E$ into the space of real-valued measurable functions on a probability space, has a measurable version with values in ${\mathbb R}^E$. Similarly, one may ask…
This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average fields…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…