相关论文: On causal band-limited mean square approximation

This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm. We prove…

Heat diffusion processes have found wide applications in modelling dynamical systems over graphs. In this paper, we consider the recovery of a $k$-bandlimited graph signal that is an initial signal of a heat diffusion process from its…

Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on the expected number of bits transmitted per second. A decoder uses the…

The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence…

Let a continuous random process $X$ defined on $[0,1]$ be $(m+\beta)$-smooth, $0\le m, 0<\beta\le 1$, in quadratic mean for all $t>0$ and have an isolated singularity point at $t=0$. In addition, let $X$ be locally like a $m$-fold…

We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\in \mathbb{N}$? We estimate the probability that a sampling inequality of the…

We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…

We propose a method to approximate continuous-time, continuous-state stochastic processes by a discrete-time Markov chain defined on a nonuniform grid. Our method provides exact moment matching for processes whose first and second moments…

We investigate time encoding as an alternative method to classical sampling, and address the problem of reconstructing classes of non-bandlimited signals from time-based samples. We consider a sampling mechanism based on first filtering the…

This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any…

This paper considers the constrained sampling multi-stream quickest change detection problem, also known as the bandit quickest change detection problem. One stream contains a change-point that shifts its mean by an unknown amount. The goal…

The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original…

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…

It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…

In this paper the problem of assessing bounds on the accuracy of pilot-based estimation of a bandlimited frequency selective communication channel is tackled. Mean square error is taken as a figure of merit in channel estimation and a…

We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities…

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

The random sampling on graph signals is one of the fundamental topics in graph signal processing. In this letter, we consider the random sampling of k-bandlimited signals from the local measurements and show that no more than O(klogk)…