On strong laws of large numbers for arrays of rowwise independent random elements.
On strong liftings for projective limits
We discuss the permanence of strong liftings under the formation of projective limits. The results are based on an appropriate consistency condition of the liftings with the projective system called "self-consistency", which is fulfilled in many situations. In addition, we study the relationship of self-consistency and completion regularity as well as projective limits of lifting topologies.
On strong Markov duals.
On subexponential distributions and asymptotics of the distribution of the maximum of sequential sums.
On subexponentiality of the Lev́y measure of the inverse local time; with applications to penalizations.
On subordinators, self-similar Markov processes and some factorizations of the exponential variable.
On subsets of and -stable processes
On sums of dependent uniformly distributed random variables.
We study and solve several functional equations which yield necessary and sufficient conditions for the sum of two uniformly distributed random variables to be uniformly distributed.
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 surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity
We study linear stability of solutions to the Navier-Stokes equations with stochastic viscosity. Specifically, we assume that the viscosity is given in the form of a stochastic expansion. Stability analysis requires a solution of the steady-state Navier-Stokes equation and then leads to a generalized eigenvalue problem, from which we wish to characterize the real part of the rightmost eigenvalue. While this can be achieved by Monte Carlo simulation, due to its computational cost we study three surrogates...
On symmetric stable random variables and matrix transposition
On system reliability under random load of elements
On tails of stationary measures on a class of solvable groups
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 Talagrand's deviation inequalities for product measures
On Talagrand's deviation inequalities for product measures
We present a new and simple approach to some of the deviation inequalities for product measures deeply investigated by M. Talagrand in the recent years. Our method is based on functional inequalities of Poincaré and logarithmic Sobolev type and iteration of these inequalities. In particular, we establish with theses tools sharp deviation inequalities from the mean on norms of sums of independent random vectors and empirical processes. Concentration for the Hamming distance may also be deduced...
On Tchebycheff's type inequalities.
Three inequalities of Tchebycheff type are presented. Two of them give lower bounds for the probability of intervals not necessarily symmetric around the mean. The third one generalizes the extension of Tchebycheff's inequalities given by Miyamoto (1978). They are based on the inequality of Markov. Attainability of lower bounds is also discussed.
On testing of general random closed set model hypothesis
A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set with values in the extended convex ring is introduced. The method is based on the summary statistics – normalized intrinsic volumes densities of the -parallel sets to . The estimated summary statistics are compared with theirs envelopes produced from simulations of the model given by the tested hypothesis. The p-level of the test is then computed via approximation...