Pierre-Olivier Amblard

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Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks can be used to assess Granger causality graphs of stochastic processes. We show that directed information theory(More)
This paper is devoted to the study of higher-order statistics for complex random variables. We introduce a general framework allowing the direct manipulation of complex quantities: the separation between the real and the imaginary parts of a variable is avoided. We give the rules to integrate and derive probability density functions and characteristic(More)
This report reviews the conceptual and theoretical links between Granger causality and directed information theory. We begin with a short historical tour of Granger causality, concentrating on its closeness to information theory. The definitions of Granger causality based on prediction are recalled, and the importance of the observation set is discussed. We(More)
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a <i>p</i>-multivariate self-similar Gaussian process parameterized by <i>p</i> different Hurst exponents <i>Hi</i>, <i>p</i> scaling coefficients &#x03C3;<i>i</i>(More)
This paper deals with the use of stochastic resonance (SR) for detection purposes. The nonlinear physical phenomenon of SR generally occurs in dynamical bistable systems excited by a noisy sine: such systems are able to force cooperation between sine and noise such that the noise ampli1es the sine. Because of this non-intuitive e3ect, the use of SR can be(More)