Statistical linear spaces. I. Properties of , -topology
Statistiques sur le groupe symétrique
Stochastic antiderivational equations on non-Archimedean Banach spaces.
Structural relation
Sulla assoluta continuità di una variabile aleatoria la cui densità è limite di una successione di densità costanti a tratti
Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi
Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positive density for sums of s pseudo sth powers when s ≥ 3. Moreover, our approach supports a conjecture of...
Tail probability estimates for certain Rademacher sums
The expected number of zeros of a random system of -adic polynomials.
The optional sampling theorem for convex set valued martingales.
The Poisson boundary of random rational affinities
We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all -adic fileds.
The Ray space of a right process
Let be a process with state space satisfying (a somewhat relaxed version of) Meyer’s “hypothèses droites”. Then by introducing a new topology (called the Ray topology) on and a compactification of in the Ray topology one can regard as a Ray process. However, this construction depends on the choice of an arbitrary uniformity on and not just the topology of . We show that the Ray topology is independent of the choice of this uniformity. We then introduce a space (the Ray space) which...
The tail -fields of recurrent Markov processes
Théorème de Riesz pour des processus réels
Théorie unifiée des capacités et des ensembles analytiques
Topologies du type de Skorohod
Triangle functions and composition of probability distribution functions.
The equations of left and right distributivity of composition of distribution functions over triangle functions are solved in a restricted domain.
Two Kinds of Invariance of Full Conditional Probabilities
Let G be a group acting on Ω and ℱ a G-invariant algebra of subsets of Ω. A full conditional probability on ℱ is a function P: ℱ × (ℱ∖{∅}) → [0,1] satisfying the obvious axioms (with only finite additivity). It is weakly G-invariant provided that P(gA|gB) = P(A|B) for all g ∈ G and A,B ∈ ℱ, and strongly G-invariant provided that P(gA|B) = P(A|B) whenever g ∈ G and A ∪ gA ⊆ B. Armstrong (1989) claimed that weak and strong invariance are equivalent, but we shall show that this is false and that weak...
Une classe de processus de Markov en mécanique relativiste. Laplaciens généralisés sur les espaces symétriques de type non compact
Universality for random tensors
We prove two universality results for random tensors of arbitrary rank . We first prove that a random tensor whose entries are independent, identically distributed, complex random variables converges in distribution in the large limit to the same limit as the distributional limit of a Gaussian tensor model. This generalizes the universality of random matrices to random tensors. We then prove a second, stronger, universality result. Under the weaker assumption that the joint probability distribution...
Variabili casuali deboli