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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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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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A Poisson Structure in White-Noise Analysis
AIP Conference Proceedings, 2009We define a Kirillov‐Konstant‐Souriau Poisson structure on a Hida Fock space.We define a Kirillov‐Konstant‐Souriau Poisson structure on a Hida Fock space.
R. Léandre +5 more
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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 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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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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Causal Analysis in Terms of White Noise
1980Functionals of Brownian motion, call them Brownian functionals, are discussed, where development of time is taken into account. In the course of the analysis we are naturally led to introduce classes of generalized Brownian functionals and to discuss differential calculus, where the integral representation of Brownian functionals and Levy’s functional ...
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White-noise analysis in retinal physiology
Neuroscience Research Supplements, 1986M, Sakuranaga, Y, Ando, K, Naka
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