Pierre Priouret

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In this paper we address the problem of the stability and convergence of the stochastic approximation procedure θn+1 = θn + γn+1[h(θn)+ξn+1]. The stability of such sequences {θn} is known to heavily rely on the behaviour of the mean field h at the boundary of the parameter set and the magnitude of the stepsizes used. The conditions typically required to(More)
In this paper, Smale’s α theory is generalized to the context of intrinsic Newton iteration on geodesically complete analytic Riemannian and Hermitian manifolds. Results are valid for analytic mappings from a manifold to a linear space of the same dimension, or for analytic vector fields on the manifold. The invariant γ is defined by means of high order(More)
In this paper, a perturbation expansion technique is introduced to decompose the tracking error of a general adaptive tracking algorithm in a linear regression model. This method allow to obtain tracking error bound but also tight approximate expressions for the moments of the tracking error. These expressions allow to evaluate, both qualitatively and(More)
Fluid limit techniques have become a central tool to analyze queueing networks over the last decade, with applications to performance analysis, simulation and optimization. In this paper, some of these techniques are extended to a general class of skip-free Markov chains. As in the case of queueing models, a fluid approximation is obtained by scaling time,(More)
Nf (z) = expz(−Df(z)f(z)) where expz : TzMn → Mn denotes the exponential map. When, instead of a mapping we consider a vector field X, in order to define Newton method, we resort to an object studied in differential geometry; namely, the covariant derivative of vector fields denoted here by DX. We let NX(z) = expz(−DX(z)X(z)). These definitions coincide(More)
Abstract. Fluid limit techniques have become a central tool to analyze queueing networks over the last decade, with applications to performance analysis, simulation, and optimization. In this paper some of these techniques are extended to a general class of skip-free Markov chains. As in the case of queueing models, a fluid approximation is obtained by(More)
Fluid limit techniques have become a central tool to analyze queueing networks over the last decade, with applications to performance analysis, simulation, and optimization.In this paper some of these techniques are extended to a general class of skip-free Markov chains. As in the case of queueing models, a fluid approximation is obtained by scaling time,(More)
1. Complexity theory 3 1.1. Malajovich, G and Meer, K: On the structure of NP (C). SIAM Journal on Computing 28(1), pp 27-35, Feb 1999. 3 1.2. Malajovich, G: On a Transfer Theorem for the P 6= NP Conjecture. Journal of Complexity 17 No 1, pp.27-85, 2001. 4 1.3. Malajovich, G: Lower bounds for some decision problems over C. Theoretical Computer Science 276(More)
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