Limiting behaviour of moving average processes based on a sequence of mixing and negatively associated random variables.
Limiting curlicue measures for theta sums
We consider the ensemble of curves {γα, N: α∈(0, 1], N∈ℕ} obtained by linearly interpolating the values of the normalized theta sum N−1/2∑n=0N'−1exp(πin2α), 0≤N'<N. We prove the existence of limiting finite-dimensional distributions for such curves as N→∞, when α is distributed according to any probability measure λ, absolutely continuous w.r.t. the Lebesgue measure on [0, 1]. Our Main Theorem generalizes a result by Marklof [Duke Math. J.97 (1999) 127–153] and Jurkat and van Horne [Duke...
Limiting distribution for a simple model of order book dynamics
A continuous-time model for the limit order book dynamics is considered. The set of outstanding limit orders is modeled as a pair of random counting measures and the limiting distribution of this pair of measure-valued processes is obtained under suitable conditions on the model parameters. The limiting behavior of the bid-ask spread and the midpoint of the bid-ask interval are also characterized.
Limiting properties of the k-th record values
Limiting spectral distribution of circulant type matrices with dependent inputs.
Limiting spectral distribution of XX' matrices
The methods to establish the limiting spectral distribution (LSD) of large dimensional random matrices includes the well-known moment method which invokes the trace formula. Its success has been demonstrated in several types of matrices such as the Wigner matrix and the sample covariance matrix. In a recent article Bryc, Dembo and Jiang [Ann. Probab.34 (2006) 1–38] establish the LSD for random Toeplitz and Hankel matrices using the moment method. They perform the necessary counting of terms in the...
Linear comparative calibration with correlated measurements
The paper deals with the linear comparative calibration problem, i. e. the situation when both variables are subject to errors. Considered is a quite general model which allows to include possibly correlated data (measurements). From statistical point of view the model could be represented by the linear errors-in-variables (EIV) model. We suggest an iterative algorithm for estimation the parameters of the analysis function (inverse of the calibration line) and we solve the problem of deriving the...
Linear rescaling of the stochastic process
Discussion on the limits in distribution of processes under joint rescaling of space and time is presented in this paper. The results due to Lamperti (1962), Weissman (1975), Hudson Mason (1982) and Laha Rohatgi (1982) are improved here.
Linear speed large deviations for percolation clusters.
Local central limit theorem for first entrance of a random walk into a half space
Local Conditional Expectations and an Application to a Central Limit Theorem on a Locally Compact Abelian Group.
Local extinction for superprocesses in random environments.
Local limit approximations for Lagrangian distributions.
Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX
We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional: . On the other hand, we describe Feynman-Kac type penalisation results for long Brownian bridges thus completing some similar previous study for standard Brownian motion (see [B. Roynette, P. Vallois and M. Yor, Studia Sci. Math. Hung.43 (2006) 171–246]).
Local limit theorems for non-identical integer valued random variables, to appear theory probability. Applications
Localization and delocalization for heavy tailed band matrices
We consider some random band matrices with band-width whose entries are independent random variables with distribution tail in . We consider the largest eigenvalues and the associated eigenvectors and prove the following phase transition. On the one hand, when , the largest eigenvalues have order , are asymptotically distributed as a Poisson process and their associated eigenvectors are essentially carried by two coordinates (this phenomenon has already been remarked for full matrices by Soshnikov...
Loi du logarithme itère pour certaines intégrales stochastiques
Loi du logarithme itère pour les suites de vecteurs gaussiens
Loi du “tout ou rien” dans un jeu de pile ou face
Loi multidimensionnelle de Cauchy comme une distribution limite des sommes de vecteurs aléatoires dépendants