White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.

Enhancement of stability in randomly switching potential with metastable state

Abstract: The overdamped motion of a Brownian particle in randomly switching piece-wise metastable linear potential shows noise enhanced stability (NES): the noise stabilizes the metastable system and the system remains in this state for a longer time than in the absence of white noise. The mean first passage time (MFPT) has a maximum at a finite value of white noise intensity. The analytical expression of MFPT in terms of the white noise intensity, the parameters of the potential barrier, and of the dichotomous noise is derived. The conditions for the NES phenomenon and the parameter region where the effect can be observed are obtained. The mean first passage time behaviors as a function of the mean flipping rate of the potential for unstable and metastable initial configurations are also analyzed. We observe the resonant activation phenomenon for initial metastable configuration of the potential profile.

Stochastic resonance driven by time-modulated correlated white noise sources

Abstract: We analyze the effects caused by the simultaneous presence of correlated additive and multiplicative noises for stochastic resonance. Besides the standard potential modulation we also consider a time-periodic variation of the correlation between the two noise sources. As a foremost result we find that stochastic resonance, as characterized by the signal-to-noise ratio and the spectral amplification, becomes characteristically broadened. The broadening can be controlled by varying the relative phase shift between the two types of modulation force.

The Estimation of Open Higher-Order Continuous Time Dynamic Models with Mixed Stock and Flow Data

Abstract: This article extends recent work on the Gaussian or quasi-maximum likelihood estimation of the parameters of a closed higher-order continuous time dynamic model by introducing exogenous variables into the model. The method presented yields exact maximum likelihood estimates when the innovations are Gaussian and the exogenous variables are polynomials in time of degree not exceeding two, and it can be expected to yield very good estimates under more general conditions. It is applicable, in principle, to a system of any order with mixed stock and flow data. The precise formulas for its implementation are derived, in this article, for a second-order system in which both the endogenous and exogenous variables are a mixture of stock and flow variables. In two recent articles [3, 5] I have developed a method of obtaining Gaussian or quasi-maximum likelihood estimates of the parameters of a closed higherorder continuous time dynamic model from discrete data. The theoretical foundations for the method are provided in [3] with the proof of an existence and uniqueness theorem for the solution of the model under the most general assumptions about the white noise innovation process, and without assuming that the system is stationary or even stable. The assumptions about the innovation process include the case in which the innovations are a mixture of Brownian motion and Poisson processes and allow for more general innovation processes in which the increments are not independent but merely

More on autoregressive model fitting with noisy data by Akaike's information criterion (Corresp.)

Abstract: Davisson [131, [141 has considered the problem of determining the "order" of the signal from noisy data. Although interesting theoretically, his result is difficult to use in practice. In this correspondence, we exploit one well-known fact concerning autoregressive (AR) signals plus white noise, and using Akaike's information criterion [15], [17], we have developed one efficient procedure for determining the order of the AR signal from noisy data. The procedure is illustrated numerically using both artificially generated and real data. The connection between the preceding problem and the classical statistical problem of factor analysis is discussed.

Memory Limited, Streaming PCA

Abstract: We consider streaming, one-pass principal component analysis (PCA), in the high-dimensional regime, with limited memory. Here, p-dimensional samples are presented sequentially, and the goal is to produce the k-dimensional subspace that best approximates these points. Standard algorithms require O(p2) memory; meanwhile no algorithm can do better than O(kp) memory, since this is what the output itself requires. Memory (or storage) complexity is most meaningful when understood in the context of computational and sample complexity. Sample complexity for high-dimensional PCA is typically studied in the setting of the spiked covariance model, where p-dimensional points are generated from a population covariance equal to the identity (white noise) plus a low-dimensional perturbation (the spike) which is the signal to be recovered. It is now well-understood that the spike can be recovered when the number of samples, n, scales proportionally with the dimension, p. Yet, all algorithms that provably achieve this, have memory complexity O(p2). Meanwhile, algorithms with memory-complexity O(kp) do not have provable bounds on sample complexity comparable to p. We present an algorithm that achieves both: it uses O(kp) memory (meaning storage of any kind) and is able to compute the k-dimensional spike with O(p log p) sample-complexity - the first algorithm of its kind. While our theoretical analysis focuses on the spiked covariance model, our simulations show that our algorithm is successful on much more general models for the data.