Moderate deviations in a random graph and for the spectrum of Bernoulli random matrices.
Moderate Growth and Random Walk on Finite Groups.
Moment functions and laws of large numbers on hypergroups.
Moment inequalities connected with accompanying Poisson laws in Abelian groups.
Moments of probability measures on a group.
Multiplications aléatoires et dimensions de Hausdorff
Multiplicative semigroups of infinite dimensional matrices.
Multiply self-decomposable measures in generalized convolution algebras
Multiply self-decomposable probability measures on Banach spaces
Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation
In [A. Genadot and M. Thieullen, Averaging for a fully coupled piecewise-deterministic markov process in infinite dimensions. Adv. Appl. Probab. 44 (2012) 749–773], the authors addressed the question of averaging for a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimensions. In the present paper, we carry on and complete this work by the mathematical analysis of the fluctuations of the slow-fast system around the averaged limit. A central limit theorem is derived and the associated...
Multistage multivariate nested distance: An empirical analysis
Multistage stochastic optimization requires the definition and the generation of a discrete stochastic tree that represents the evolution of the uncertain parameters in time and space. The dimension of the tree is the result of a trade-off between the adaptability to the original probability distribution and the computational tractability. Moreover, the discrete approximation of a continuous random variable is not unique. The concept of the best discrete approximation has been widely explored and...
Multivariate copulas: Transformations, symmetry, order and measures of concordance
The present paper introduces a group of transformations on the collection of all multivariate copulas. The group contains a subgroup which is of particular interest since its elements preserve symmetry, the concordance order between two copulas and the value of every measure of concordance.
Multi-variate correlation and mixtures of product measures
Total correlation (‘TC’) and dual total correlation (‘DTC’) are two classical ways to quantify the correlation among an -tuple of random variables. They both reduce to mutual information when . The first part of this paper sets up the theory of TC and DTC for general random variables, not necessarily finite-valued. This generality has not been exposed in the literature before. The second part considers the structural implications when a joint distribution has small TC or DTC. If , then is...
Multivariate tail equivalence of distributions in extreme value theory
New metrics for weak convergence of distribution functions.
Sibley and Sempi have constructed metrics on the space of probability distribution functions with the property that weak convergence of a sequence is equivalent to metric convergence. Sibley's work is a modification of Levy's metric, but Sempi's construction is of a different sort. Here we construct a family of metrics having the same convergence properties as Sibley's and Sempi's but which does not appear to be related to theirs in any simple way. Some instances are brought out in which the metrics...
New sufficient conditions for the law of the iterated logarithm in Banach spaces
Non-Borel measures on non-separable metric spaces
Non-Hilbertian structure of the Wiener measure
Nonlinear diffusion with jumps
Nonlinear structures determined by measures on Banach spaces