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...