Le théorème de la limite centrale et la loi du logarithme itéré dans les espaces de Banach (suite et fin)
Le théorème de la limite centrale et la loi du logarithme itéré dans les espaces de Banach
Les algorithmes stochastiques contournent-ils les pièges ?
Les «principes d'invariance» en probabilité sur l'espace de Wiener
Level crossings and other level functionals of stationary Gaussian processes.
Lévy classes and self-normalization.
Lévy's probability measures on Euclidean spaces
Likelihood and parametric heteroscedasticity in normal connected linear models
A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.
Likely path to extinction in simple branching models with large initial population.
Limit distributions for sums of shrunken random variables [Book]
Limit laws for a coagulation model of interacting random particles
Limit laws for the energy of a charged polymer
In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy Hn=∑1≤j<k≤nωjωk1{Sj=Sk} of the polymer {S1, …, Sn} equipped with random electrical charges {ω1, …, ωn}. Our approach is based on comparison of the moments between Hn and the self-intersection local time Qn=∑1≤j<k≤n1{Sj=Sk} run by the d-dimensional random walk {Sk}. As partially needed for our main objective and partially motivated by their independent interest,...
Limit laws for transient random walks in random environment on
We consider transient random walks in random environment on with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level converges in law, after a proper normalization, towards a positive stable law, but they do not obtain a description of its parameter. A different proof of this result is presented, that leads to a complete characterization of this stable law. The case of Dirichlet environment turns out to be remarkably explicit.
Limit laws of transient excited random walks on integers
We consider excited random walks (ERWs) on ℤ with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, δ, is larger than 1 then ERW is transient to the right and, moreover, for δ>4 under the averaged measure it obeys the Central Limit Theorem. We show that when δ∈(2, 4] the limiting behavior of an appropriately centered and scaled excited random...
Limit Measures Related to the Conditionally Free Convolution
We describe the limit measures for some class of deformations of the free convolution, introduced by A. D. Krystek and Ł. J. Wojakowski. In particular, we provide a counterexample to a conjecture from their paper.
Limit probabilities for random sparse bit strings.
Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak∼Ckp−1, k→∞, p>0, where C is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations of a properly scaled partition...
Limit Theorem for High Level -upcrossings by -field
Limit theorem for random walk in weakly dependent random scenery
Let S=(Sk)k≥0 be a random walk on ℤ and ξ=(ξi)i∈ℤ a stationary random sequence of centered random variables, independent of S. We consider a random walk in random scenery that is the sequence of random variables (Un)n≥0, where Un=∑k=0nξSk, n∈ℕ. Under a weak dependence assumption on the scenery ξ we prove a functional limit theorem generalizing Kesten and Spitzer’s [Z. Wahrsch. Verw. Gebiete50 (1979) 5–25] theorem.
Limit theorem in the space of continuous functions for the Dirichlet polynomial related with the Riemann zeta-funtion
A limit theorem in the space of continuous functions for the Dirichlet polynomialwhere denote the coefficients of the Dirichlet series expansion of the function in the half-plane