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Search Results: 1 - 10 of 8206 matches for " Michel Fliess "
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Analyse non standard du bruit
Michel Fliess
Mathematics , 2006,
Abstract: Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y. Perrin, an appropriate mathematical framework is derived for new non-asymptotic estimation techniques, which do not necessitate any statistical analysis of the noises corrupting any sensor. Various applications are deduced for multiplicative noises, for the length of the parametric estimation windows, and for burst errors.
Réflexions sur la question fréquentielle en traitement du signal
Michel Fliess
Mathematics , 2005,
Abstract: New definitions are suggested for frequencies which may be instantaneous or not. The Heisenberg-Gabor inequality and the Shannon sampling theorem are briefly discussed.
Critique du rapport signal à bruit en théorie de l'information -- A critical appraisal of the signal to noise ratio in information theory
Michel Fliess
Mathematics , 2007,
Abstract: The signal to noise ratio, which plays such an important role in information theory, is shown to become pointless in digital communications where - symbols are modulating carriers, which are solutions of linear differential equations with polynomial coefficients, - demodulations is achieved thanks to new algebraic estimation techniques. Operational calculus, differential algebra and nonstandard analysis are the main mathematical tools.
Approche intrinsèque des fluctuations quantiques en mécanique stochastique (An intrinsic approach of the quantum fluctuations in stochastic mechanics)
Michel Fliess
Mathematics , 2006,
Abstract: This note is answering an old questioning about the F\'{e}nyes-Nelson stochastic mechanics. The Brownian nature of the quantum fluctuations, which are associated to this mechanics, is deduced from Feynman's interpretation of the Heisenberg uncertainty principle via infinitesimal random walks stemming from nonstandard analysis. It is therefore no more necessary to combine those fluctuations with a background field, which has never been well understood. Most of the technical details are contained in an extended english abstract.
Probabilités et fluctuations quantiques (Probabilities and quantum fluctuations)
Michel Fliess
Mathematics , 2007,
Abstract: This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty principle, i.e., of the quantum fluctuations, which was brought to the forefront in some fractal approaches. It results, as in Nelson's stochastic mechanics, in stochastic differential equations which are deduced from infinitesimal random walks. An extended english abstract gives most of the details.
Critique du rapport signal à bruit en communications numériques -- Questioning the signal to noise ratio in digital communications
Michel Fliess
Mathematics , 2008,
Abstract: The signal to noise ratio, which plays such an important r\^ole in information theory, is shown to become pointless for digital communications where the demodulation is achieved via new fast estimation techniques. Operational calculus, differential algebra, noncommutative algebra and nonstandard analysis are the main mathematical tools.
A mathematical proof of the existence of trends in financial time series
Michel Fliess,Cédric Join
Mathematics , 2009,
Abstract: We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard Analysis in Practice, Springer, 1995, pp. 195--204). Those trends, which might coexist with some altered random walk paradigm and efficient market hypothesis, seem nevertheless difficult to reconcile with the celebrated Black-Scholes model. They are estimated via recent techniques stemming from control and signal theory. Several quite convincing computer simulations on the forecast of various financial quantities are depicted. We conclude by discussing the r\^ole of probability theory.
Systematic and multifactor risk models revisited
Michel Fliess,Cédric Join
Mathematics , 2013,
Abstract: Systematic and multifactor risk models are revisited via methods which were already successfully developed in signal processing and in automatic control. The results, which bypass the usual criticisms on those risk modeling, are illustrated by several successful computer experiments.
Time Series Technical Analysis via New Fast Estimation Methods: A Preliminary Study in Mathematical Finance
Michel Fliess,Cédric Join
Mathematics , 2008,
Abstract: New fast estimation methods stemming from control theory lead to a fresh look at time series, which bears some resemblance to "technical analysis". The results are applied to a typical object of financial engineering, namely the forecast of foreign exchange rates, via a "model-free" setting, i.e., via repeated identifications of low order linear difference equations on sliding short time windows. Several convincing computer simulations, including the prediction of the position and of the volatility with respect to the forecasted trendline, are provided. $\mathcal{Z}$-transform and differential algebra are the main mathematical tools.
Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control?
Michel Fliess,Cédric Join
Mathematics , 2009,
Abstract: We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to "intelligent" PID controllers, the tuning of which becomes quite straightforward, even with highly nonlinear and/or time-varying systems. Our main tool is a newly developed numerical differentiation. Differential algebra provides the theoretical framework. Our approach is validated by several numerical experiments.
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