Related papers: Aliasing-truncation Errors in Sampling Approximati…
The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates $L_p([0,T])$ and uniform approximations of…
We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…
Universal (pointwise uniform and time shifted) truncation error upper bounds are presented in Whittaker--Kotel'nikov--Shannon (WKS) sampling restoration sum for Bernstein function class $B_{\pi,d}^q\,,\ q \ge 1,$ $d\in \mathbb N\,,$ when…
Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker--Kotel'nikov--Shannon (WKS) sampling restoration sum for Bernstein function classes $B_{\pi,d}^q,\, q>1,\, d\in \mathbb N$, when…
We consider the problem of reconstructing a wide sense stationary band-limited process from its local averages taken either at the Nyquist rate or above. As a result, we obtain a sufficient condition under which average sampling expansions…
Advances of information-theoretic understanding of sparse sampling of continuous uncoded signals at sampling rates exceeding the Landau rate were reported in recent works. This work examines sparse sampling of coded signals at sub-Landau…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
We consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory convergence rate due to the slow decay of the sinc function. To…
Recently efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized…
We characterize the fundamental limits of high-dimensional mean testing under arbitrary truncation, where samples are drawn from the conditional distribution $P(\cdot \mid S)$ for an unknown truncation set $S$ that may hide up to an…
Most existing bounds for signal reconstruction from compressive measurements make the assumption of additive signal-independent noise. However in many compressive imaging systems, the noise statistics are more accurately represented by…
Stochastic processes are often represented through orthonormal series expansions, a framework originating in the classical works of Lo\`eve and Karhunen and widely used for simulation and numerical approximation. While truncation error in…
We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…
Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
A rigorous convergence analysis of the Strang splitting algorithm with a discontinuous Galerkin approximation in space for the Vlasov--Poisson equations is provided. It is shown that under suitable assumptions the error is of order…
One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (of…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
We study the problem of estimating the mean of an identity covariance Gaussian in the truncated setting, in the regime when the truncation set comes from a low-complexity family $\mathcal{C}$ of sets. Specifically, for a fixed but unknown…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…