Occupation laws for some time-nonhomogeneous Markov chains.
Occupation times of compact sets by planar brownian motion
Occurrence of rare events in ergodic interacting spin systems
On a characterization of orthogonality with respect to particular sequences of random variables in
This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results on equidistant systems of points in a Hilbert space to the case of the space of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular sequence of random variables (elements of which are taken from sets of equidistant elements of ) to be orthogonal to some other sequence in . The result obtained is interesting...
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 gap series of Mark Kac
Mark Kac gave an example of a function f on the unit interval such that f cannot be written as f(t)=g(2t)-g(t) with an integrable function g, but the limiting variance of vanishes. It is proved that there is no measurable g such that f(t)=g(2t)-g(t). It is also proved that there is a non-measurable g which satisfies this equality.
On a generalization of a theorem of W. Sudderth and some applications
On a limit theorem for random sequences.
On a multivariate version of Bernstein's inequality.
On a probability problem connected with railway traffic.
On a Stochastic Approximation Procedure Based on Averaging.
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 almost sure convergence of vector valued pramarts and multivalued pramarts.
On an Estimate of the Remainder in the Central Limit Theorem
On an exponential inequality and a strong law of large numbers for monotone measures
An exponential inequality for Choquet expectation is discussed. We also obtain a strong law of large numbers based on Choquet expectation. The main results of this paper improve some previous results obtained by many researchers.
On an invariance principle for phase separation lines
On approximate large deviations for 1D diffusion.
On Approximating the Distributions of Friedman's xr2 and Related Statistics.