We show that the Feigenbaum-Cvitanović equation can be interpreted as a linearizing equation, and the domain of analyticity of the Feigenbaum fixed point of renormalization as a basin of attraction. There is a natural decomposition of this basin which enables to recover a result of local connectivity by Jiang and Hu for the Feigenbaum Julia set.

We derive Donsker-Vardhan type results for functionals of the occupation times when the underlying random walk on Z is in the domain of attraction of an operatorstable law on R. Applications to random walks on wreath products (also known as lamplighter groups) are given.

We consider the asymptotic behavior of additive functionals of linear processes with infinite variance innovations. Applying the central limit theory for Markov chains, we establish asymptotic normality for short-range dependent processes. A non-central limit theorem is obtained when the processes are long-range dependent and the innovations are in the domain of attraction of stable laws.

2014 The domain of attraction of a neural network memory fixed point is computed as a function of its local magnetic fields. When combined with standard learning algorithms, the result makes it possible to construct saturated associative networks memories with precisely specified recall properties. J. Phys. France 49 (1988) 1657-1662 OCTOBRE 1988, Classification Physics Abstracts ’ 75.10H 87.30...

We consider an Ornstein-Uhleneck process associated to self-normalized sums in i.i.d. symmetric random variables from the domain of attraction of N(0, 1) distribution. The proofs use recursive equations similar to those that arise in the area of stochastic approximation.

Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations the tail cumulative distribution functions extreme value domain attraction to directly establish asymptotic value, not necessarily type and their rates convergences. Results beyond are provided. Explicit concerning very usual related convergence listed well. Some ...

This paper is devoted to the grazing collision limit of the inelastic Kac model introduced in [PT04], when the equilibrium distribution function is a heavy-tailed Lévy-type distribution with infinite variance. We prove that solutions in an appropriate domain of attraction of the equilibrium distribution converge to solutions of a Fokker-Planck equation with a fractional diffusion operator.

Abstract: Let X be a generalised symmetrised Dirichlet random vector inIR, k ≥ 2, and let tn ∈IRk, n ≥ 1 be such that limn→∞ P {X > tn} = 0. In this paper we derive an exact asymptotic expansion of P {X > tn} as n → ∞, assuming that the associated random radius of X has distribution function in the Gumbel max-domain of attraction.

As Bleher, [B 92] observed the free flight vector of the planar, infinite horizon, periodic Lorentz process {Sn|n = 0, 1, 2, . . . } belongs to the nonstandard domain of attraction of the Gaussian law — actually with the √ n log n scaling. Our first aim is to establish his conjecture that, indeed, Sn

It is proved that if the multivariate Student t-statistic based on i.i.d. symmetric random vectors is asymptotically standard normal, then these random vectors are in the generalized domain of attraction of the normal law. Uniform integrability is also considered, even in the absence of symmetry.