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A Unified Characterization Theorem in White Noise Theory
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2003We revisit a CKS-space from the viewpoint of standard setup of white noise calculus and prove a general characterization theorem for white noise operators from a CKS-space into another CKS-space. The usual characterizations so far obtained for white noise distributions, white noise test functions and white noise operators are all consequences of the ...
Ji, Un Cig, Obata, Nobuaki
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Unified Theory of Oscillator Phase Noise I: White Noise
IEEE Transactions on Microwave Theory and Techniques, 2013The spectral purity of every oscillator system is limited by phase noise. In this work, we extend the techniques previously used to analyze phase noise in lasers to develop an intuitive, yet powerful description of phase noise in an electromagnetic oscillator for the case when the oscillating field is sinusoidal and perturbed by white noise.
William Loh +3 more
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White Noise Stochastic BVP’s and Cimmino’s Theory
2001The analysis of the Molodensky problem in spherical approximation can be reduced to the simple Dirichlet problem. If the boundary data are noisy (white noise), it is requested to explain what is the meaning of the solution of a B.V.P. with data of this kind.
SANSO', FERNANDO, VENUTI, GIOVANNA
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General Theory of White Noise Analysis
2000White noise analysis was initiated by T. Hida in 1975. This is an infinite dimensional stochastic analysis, the basic idea of which is to view Wiener functionals as functionals of white noise. More precisely, let Ω denote the space of all continuous functions f on ∝, null at 0, equipped with the topology of uniform convergence on bounded sets.
Zhi-yuan Huang, Jia-an Yan
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External non-white noise: Theory and experiment
Physica A: Statistical Mechanics and its Applications, 1982Abstract We consider a system under the influence of an external gaussian noise with a flat spectrum and finite cut-off frequency. The stationery properties of the system are studied as a function of the correlation time of the noise. Theoretical predictions based on an expansion in powers of the correlation time are corroborated by experimental ...
J.M. Sancho +3 more
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CHARACTERIZATION THEOREMS IN GEGENBAUER WHITE NOISE THEORY
Quantum Probability and Related Topics, 2008The main purpose of this paper is to derive a general structure of Gegenbauer white noise analysis as a counterpart class of non-Levy white noise. Namely, we consider, on an appropriate space of distributions, N ′ β , a Gegenbauer white noise measure, Gβ , and construct a nuclear triple (Nβ) ⊂ L2(N ′ β ,Gβ) ⊂ (Nβ)∗ of test and generalized functions.
A. BARHOUMI, A. RIAHI, H. OUERDIANE
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White-Noise Analysis of a Neuron Chain: An Application of the Wiener Theory
Science, 1972The Wiener theory of nonlinear system identification was applied to a three-stage neuron chain in the catfish retina in order to determine the functional relationship between the artificial polarization of the horizontal cell membrane potential and the resulting discharge of the ganglion cell.
P Z, Marmarelis, K, Naka
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SOME OF FUTURE DIRECTIONS OF WHITE NOISE THEORY
Quantum Information and Computing, 2006Some of future directions of white noise analysis will be presented. First, we shall revisit the space of generalized white noise functionals with a view point of analogue calculus. It is reasonable, in fact, not too large, once the system of variables is taken to be white noise {Ḃ(t), t ∈ R1}.
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Characteristics of Response to Nonstationary White Noise: Theory
Journal of Engineering Mechanics, 1989New methods of analysis are developed to study characteristics of the response of linear systems to nonstationary stochastic input. An envelope of the response based on the Hilbert transformation of the process is used, and derivations are made with respect to stationary response properties.
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White noise and heating of quantum field theory in an open system
Physical Review D, 1991The time evolution of the density matrix of a relativistic quantum field theory coupled to random noise is discussed. Using path-integral techniques, we solve analytically for the density matrix of a system of free fields coupled to noise. We show that in the limit of large time the density matrix evolves to a thermal state and we compute the ...
, Cloutier, , Semenoff
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