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White noise
About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.
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TL;DR: In this paper, the spatial and time regularity of solutions to linear stochastic evolution equations perturbed by Levy white noise is investigated and sufficient conditions for spatial continuity are derived.
Abstract: The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by Levy white noise “obtained by subordination of a Gaussian white noise”. Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.
84 citations
TL;DR: In this article, the authors prove existence and uniqueness of the solution of a white noise driven parabolic SPDE, in case the drift is measurable and satisfies a "one sided linear growth condition," and the diffusion coefficient is non-degenerate, has a locally Lipschitz derivative, and satisfies linear growth conditions.
84 citations
TL;DR: Two techniques for upper bounding the average probability of decoding error in coded modulation structures are presented and it is shown that for the Leech lattice this upper bound is very close to a sphere lower bound.
Abstract: Two techniques for upper bounding the average probability of decoding error in coded modulation structures are presented. The first bound, which is applicable to the additive white Gaussian noise (AWGN) channel, is tighter than the well-known union bound and the minimum distance bound, especially for low signal to noise ratio. It is shown that for the Leech lattice this upper bound is very close to a sphere lower bound. For the second upper bound, which is applicable to any memoryless channel (not necessarily AWGN), a method of random coset coding is presented. For the AWGN channel, a tighter upper bound is obtained by employing the method of random coset coding for calculating the average spectrum of distances of the code, which is required for the computation of the first upper bound. >
84 citations
TL;DR: This contribution provides formal results for convergence and asymptotic optimality of an adaptive input design method based on the certainty equivalence principle, i.e. for each time step an optimal input design problem is solved exactly using the present parameter estimate.
84 citations
11 Dec 1996
TL;DR: In this article, the authors report the development of full and reduced order linear unbiased estimators for discrete-time stochastic parameter systems and show how to parametrize the estimator gains to achieve a certain estimation error covariance.
Abstract: The motivation for the work reported in this paper accrues from the necessity of finding stabilizing control laws for systems with randomly varying distributed delays. It reports the development of full and reduced order linear unbiased estimators for discrete-time stochastic parameter systems and shows how to parametrize the estimator gains to achieve a certain estimation error covariance. Both finite-time and steady-state estimators are considered. The results are potentially applicable to state-estimate feedback control schemes for such systems.
84 citations