منابع مشابه
Itô calculus and quantum white noise calculus
Itô calculus has been generalized in white noise analysis and in quantum stochastic calculus. Quantum white noise calculus is a third generalization, unifying the two above mentioned ones and bringing some unexpected insight into some old problems studied in different fields, such as the renormalization problem in physics and the representation theory of Lie algebras. The present paper is an at...
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Based on an adequate new Gel’fand triple, we construct the infinite dimensional free Gaussian white noise measure μ using the Bochner-Minlos theorem. Next, we give the chaos decomposition of an L2 space with respect to the measure μ .
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We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a Gaussian random field indexed by a measure space. We then show how existing theory for integration with respect to Gaussian processes indexed by [0, 1] can be ...
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Autoregressive (AR) modeling is widely used in signal processing. The coefficients of an AR model can be easily obtained with a least mean square (LMS) prediction error filter. However, it is known that this filter gives a biased solution when the input signal is corrupted by white Gaussian noise. Treichler suggested the -LMS algorithm to remedy this problem and proved that the mean weight vect...
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Abstract. A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick’s and Ito’s theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and the conditions for unitarity have been proven. The Hamiltonian of the associated one parameter strongly continuous group has been calculated expli...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1980
ISSN: 0386-2194
DOI: 10.3792/pjaa.56.411