On the Azéma martingales
On the Azéma-Yor stopping time
On the Barlow-Yor inequalities for local time
On the Bennett–Hoeffding inequality
The well-known Bennett–Hoeffding bound for sums of independent random variables is refined, by taking into account positive-part third moments, and at that significantly improved by using, instead of the class of all increasing exponential functions, a much larger class of generalized moment functions. The resulting bounds have certain optimality properties. The results can be extended in a standard manner to (the maximal functions of) (super)martingales. The proof of the main result relies on an...
On the boundedness of Bernoulli processes over thin sets.
On the central limit problem for processes of zero entropy
On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups.
On the comparison of pure jump processes
On the computation of the exact distribution of power divergence test statistics
In this paper we introduce several algorithms to generate all the vectors in the support of a multinomial distribution. Computational studies are carried out to analyze their efficiency with respect to the CPU time and to calculate their efficiency frontiers. The proposed algorithm is used to calculate exact distributions of power divergence test statistics under the hypothesis of uniformity. Finally, several exact power comparisons are done for different divergence statistics and families of alternatives...
On the concept of the asymptotic Rényi distances for random fields
The asymptotic Rényi distances are explicitly defined and rigorously studied for a convenient class of Gibbs random fields, which are introduced as a natural infinite-dimensional generalization of exponential distributions.
On the conditional intensity of a random measure
We prove the existence of the conditional intensity of a random measure that is absolutely continuous with respect to its mean; when there exists an L-intensity, , the conditional intensity is obtained at the same time almost surely and in the mean.
On the Construction of Random Measures
On the continuity property of Gaussian random fields
On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms
We study the almost sure asymptotic behaviour of stochastic approximation algorithms for the search of zero of a real function. The quadratic strong law of large numbers is extended to the powers greater than one. In other words, the convergence of moments in the almost sure central limit theorem (ASCLT) is established. As a by-product of this convergence, one gets another proof of ASCLT for stochastic approximation algorithms. The convergence result is applied to several examples as estimation...
On the convergence of moments in the CLT for triangular arrays with an application to random polynomials
We give a proof of convergence of moments in the Central Limit Theorem (under the Lyapunov-Lindeberg condition) for triangular arrays, yielding a new estimate of the speed of convergence expressed in terms of νth moments. We also give an application to the convergence in the mean of the pth moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.
On the convergence of the ensemble Kalman filter
Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and bounds on the ensemble then give convergence.
On the coupling property of Lévy processes
We give necessary and sufficient conditions guaranteeing that the coupling for Lévy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall–Rogers on couplings of random walks. In particular, we obtain that a Lévy process admits a successful coupling, if it is a strong Feller process or if the Lévy (jump) measure has an absolutely continuous component.
On The Decomposition Of Arbitrary Second Ordered Stochastic Process
On the density of log concave seminorms on vector spaces
On the detection of a complex finite binary sequence in the presence of an interfering complex binary sequence