On stationarity of a multiple doubly stochastic model
On strictly sparse subsets of a free group.
On subexponential distributions and asymptotics of the distribution of the maximum of sequential sums.
On subsets of and -stable processes
On sums of i.i.d. random variables indexed by N parameters
On sums of independent random variables without power moments.
On suprema of Lévy processes and application in risk theory
Let X̂=C−Y where Y is a general one-dimensional Lévy process and C an independent subordinator. Consider the times when a new supremum of X̂ is reached by a jump of the subordinator C. We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and X̂ drifts to −∞, we decompose the absolute supremum of X̂ at these times, and derive a Pollaczek–Hinchin-type formula for the distribution function of the supremum.
On Talagrand's Admissible Net Approach to Majorizing Measures and Boundedness of Stochastic Processes
We show that the main result of [1] on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process with bounded...
On the accuracy of approximation of the distribution of negative-binomial random sums by the gamma distribution
The main goal of this paper is to study the accuracy of approximation for the distributions of negative-binomial random sums of independent, identically distributed random variables by the gamma distribution.
On the adaptive wavelet estimation of a multidimensional regression function under -mixing dependence: Beyond the standard assumptions on the noise
We investigate the estimation of a multidimensional regression function from observations of an -mixing process , where , represents the design and the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of in its construction) or it is supposed that is bounded or/and has a known distribution. In this paper, we go far beyond this classical framework....
On the approximate solutions of the Stratonovitch equation.
On the asymptotic behavior of the second moment of the Fourier transform of a random measure.
On the Asymptotic Behaviour of Convolution Powers of Probabilities on Discrete Groups.
On the asymptotic behaviour of increasing self-similar Markov processes.
On the asymptotic behaviour of sequences of random variables and of their previsible compensators
On the asymptotic behaviour of stationary gaussian processes
On the asymptotic equidistribution of sums of independent identically distributed random variables
On the asymptotic probability for the deviations of dependent bootstrap means from the sample mean.
On the asymptotic variance in the central limit theorem for particle filters
Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends...
On the asymptotic variance in the central limit theorem for particle filters
Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends...