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In this paper we address the problem of the stability and convergence of the stochastic approximation procedure θ n+1 = θn + γ n+1 [h(θn) + ξ n+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… (More)

- R Douc, G Fort, E Moulines, P Priouret
- 2007

The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a pathwise-type convergence of the total variation distance of the filter started from two different initial distributions , and a… (More)

In this paper, Smale's α theory is generalized to the context of intrinsic Newton iteration on geodesically complete analytic Riemannian and Her-mitian 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 talk we consider quantitative aspects of Newton method for finding zeros of analytic mappings f : M n → R n and analytic vector fields X : M n → T M n defined on a real complete analytic Riemannian manifold M n ; n is its dimension and T M n denotes its tangent bundle. We extend to this case Smale's alpha-theory introduced in [15], [16] and [17].… (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)

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)

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)

- R Aguech, E Moulines, P Priouret
- 2007

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)