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Renormalizations in White Noise Analysis
2011Renormalization has been applied in many places by using a method fitting for each situation. In this report, we are in a position where a white noise \(\{ \dot B(t), t \in R^1 \}\) is taken to be a variable system of random functions \(\varphi (\dot B).\) With this setting, renormalization plays the role that lets \(\varphi (\dot B)\) become a ...
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White Noise Analysis and Applications
1994This article presents some of the recent development in white noise analysis as an infinite dimensional calculus.
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White Noise Analysis and the Levy Laplacian
1988In line with the harmonic analysis on the space (L2)- of generalized Brownian functionals we are given the Levy’s Laplacian ΔL and discuss its roles in the causal calculus on (L2)-. There we can find interesting relations to the Levy group as well as to the Fourier transform introduced by H.-H. Kuo.
Takeyuki Hida, Kimiaki Saito
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White-Noise Analysis of Neuron Circuitry
1988White-noise analysis performed on the catfish retinal neurons has revealed that: 1) the modulation responses of horizontal and bipolar cells are linearly related to the input modulation; 2) a primordial second-order nonlinearity is generated by a class of amacrine cells, type-C cells; 3) the second-order nonlinearity observed in the other type of ...
Ken-Ichi Naka, Hiroko M. Sakai
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An Introduction to White Noise Analysis
1994The Gaussian white noise measure μ (on the Borel algebra over cylinder sets of real, tempered distributions ω ∈ S * (R d )) is conveniently described by its characteristic function: $$C(f) = E({e^{i }}) = \int\limits_{S*} {d\mu [\omega ]{e^{i }}} = {e^{ - \tfrac{1}{2}\int {{f^{2(t)dt}}} }},f \in S({R^d})$$ (1.1)
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White Noise Analysis and Chaos Expansions
2017In the framework of white noise analysis, random variables and stochastic processes can be represented in terms of Fourier series in a Hilbert space orthogonal basis, namely in their chaos expansion forms. We briefly summarize basic concepts and notations of white noise analysis, characterize different classes of stochastic processes (test, square ...
Tijana Levajković, Hermann Mena
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An Approach to a Generalization of White Noise Analysis
2009In this article, we review some recent developments in white noise analysis and its generalizations. In particular, we describe the main idea of the biorthogonal approach to a generalization of white noise analysis, connected with the theory of hypergroups.
Yu.M. Berezansky, V.A. Tesko
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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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White-noise analysis in retinal physiology
Neuroscience Research Supplements, 1986M, Sakuranaga, Y, Ando, K, Naka
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