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We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…
We develop a theory of weak Poincar\'e inequalities to characterize convergence rates of ergodic Markov chains. Motivated by the application of Markov chains in the context of algorithms, we develop a relevant set of tools which enable the…
The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this…
The paper studies the rate of convergence of the weak Euler approximation for solutions to possibly completely degenerate SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the…
We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…
This paper presents a novel approach for estimating the modes of an observed non-stationary mixture signal. A link is first established between the short-time Fourier transform and the sparse sampling theory, where the observations are…
We provide a abstract framework to prove total variation convergence result with arbitrary rate for numerical scheme for SDE. In particular we show that under standard weak approximation properties of scheme such as Euler we can obtain…
This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged "statistical"…
The accuracy of wavefront reconstruction from discrete slope measurements depends on the sampling geometry, coherence length of the incoming wavefronts, wavefront sensor specifications and the accuracy of the reconstruction algorithm. Monte…
A one-dimensional stochastic wave equation driven by a general stochastic measure is studied in this paper. The Fourier series expansion of stochastic measures is considered. It is proved that changing the integrator by the corresponding…
Poincar{\'e} inequalities are ubiquitous in probability and analysis and have various applications in statistics (concentration of measure, rate of convergence of Markov chains). The Poincar{\'e} constant, for which the inequality is tight,…
We study counterfactual stochastic optimization of conditional loss functionals under misspecified and noisy gradient information. The difficulty is that when the conditioning event has vanishing or zero probability, naive Monte Carlo…
We study the adapted solution, numerical methods, and related convergence analysis for a unified backward stochastic partial differential equation (B-SPDE). The equation is vector-valued, whose drift and diffusion coefficients may involve…
The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and…
We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…
We investigate the effect of using different distance estimators on the recovery of the peculiar velocity field of galaxies using Potent. An inappropriate choice of distance estimator will give rise to spurious flows. We discuss methods of…
We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone…
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so…