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Systems with stochastic time delay between the input and output present a number of unique challenges. Time domain noise leads to irregular alignments, obfuscates relationships and attenuates inferred coefficients. To handle these…
The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we…
Many applications, including natural language processing, sensor networks, collaborative filtering, and federated learning, call for estimating discrete distributions from data collected in batches, some of which may be untrustworthy,…
This article deals with the spatio-temporal sensors deployment in order to maximize detection probability of an intelligent and randomly moving target in an area under surveillance. Our work is based on the rare events simulation framework.…
Elliptically symmetric distributions are widely used in portfolio modeling, as well as in signal processing applications for modeling impulsive background noises. Of particular interest are algorithms for covariance estimation and subspace…
The stochastic noise of splitting, defined initially on the (basic) algebra of finite unions of intervals of the real line, is extended to a largest class of domains. The $\sigma$-fields of this largest extension constitute the completion,…
We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation algorithm, which combines statistical and computational efficiency in high-dimensions.…
In this article, we improve the Strichartz estimates obtained in [12] for the Schr\"odinger equation with white noise dispersion in one dimension. This allows us to prove global well posedness when a quintic critical nonlinearity is added…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
We study stochastically forced semilinear parabolic PDE's of the Ginzburg-Landau type. The class of forcings considered are white noises in time and colored smooth noises in space. Existence of the dynamics in $L^\infty$, as well as…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…
This paper deals with symmetric random matrices whose upper diagonal entries are obtained from a linear random field with heavy tailed noise. It is shown that the maximum eigenvalue and the spectral radius of such a random matrix with…
This paper proposes a new model called \emph{spatial continuum asymmetric channels} to study the channel capacity region of asymmetric scenarios in which either one source transmits to a spatial density of receivers or a density of…
We establish well-posedness and maximal regularity estimates for linear parabolic SPDE in divergence form involving random coefficients that are merely bounded and measurable in the time, space, and probability variables. To reach this…
We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…
We propose a phase-space formulation for the nonlinear Schr\"odinger equation with a white-noise potential in order to shed light on two issues: the rate of spread and the singularity formation in the average sense. Our main tools are the…