On a class of discrete generation interacting particle systems.
On a class of estimators in a multivariate RCA(1) model
This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...
On a limit theorem for random sequences.
On a probability problem connected with railway traffic.
On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields *
Many statistical applications require establishing central limit theorems for sums/integrals or for quadratic forms , where Xt is a stationary process. A particularly important case is that of Appell polynomials h(Xt) = Pm(Xt), h(Xt,Xs) = Pm,n (Xt,Xs), since the “Appell expansion rank" determines typically the type of central limit theorem satisfied by the functionals ST(h), QT(h). We review and extend here to multidimensional indices, along lines conjectured in [F. Avram and M.S. Taqqu,...
On a variant of random homogenization theory: convergence of the residual process and approximation of the homogenized coefficients
We consider the variant of stochastic homogenization theory introduced in [X. Blanc, C. Le Bris and P.-L. Lions, C. R. Acad. Sci. Série I 343 (2006) 717–724.; X. Blanc, C. Le Bris and P.-L. Lions, J. Math. Pures Appl. 88 (2007) 34–63.]. The equation under consideration is a standard linear elliptic equation in divergence form, where the highly oscillatory coefficient is the composition of a periodic matrix with a stochastic diffeomorphism. The homogenized limit of this problem has been identified...
On an Estimate of the Remainder in the Central Limit Theorem
On Approximating the Distributions of Friedman's xr2 and Related Statistics.
On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums
Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the Zolotarev probability...
On asymptotic normality for M-dependent U-statistics.
On asymptotic properties of the rank of a special random adjacency matrix.
On convergence in distribution of the Markov chain generated by the filter kernel induced by a fully dominated Hidden Markov Model [Book]
On convergence of population processes in random environments to the stochastic heat equation with colored noise.
On convergence of series of random elements via maximal moment relations with applications to martingale convergence and to convergence of series with -orthogonal summands.
On convergence of series of random elements via maximal moment relations with applications to martingale convergence and to convergence of series with -orthogonal summands. Correction.
On diffusivity of a tagged particle in asymmetric zero-range dynamics
On extremal measures for conservative particle systems
On Feller's criterion for the law of the iterated logarithm.
On Functional of Order Statistics.
On general asymptotic behaviour of order statistics with random index.