The martingale problem with sticky reflection conditions, and a system of particles interacting at the boundary
The Minlos lemma for positive-definite functions on additive subgroups of
Let H be a real Hilbert space. It is well known that a positive-definite function φ on H is the Fourier transform of a Radon measure on the dual space if (and only if) φ is continuous in the Sazonov topology (resp. the Gross topology) on H. Let G be an additive subgroup of H and let (resp. ) be the character group endowed with the topology of uniform convergence on precompact (resp. bounded) subsets of G. It is proved that if a positive-definite function φ on G is continuous in the Gross topology,...
The optional sampling theorem for convex set valued martingales.
The Order Aspect of the Fuzzy Real Line.
The Poisson Boundary of Polycyclic Groups
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 Pólya characterization of a Gaussian measure on groups
The product-decomposability of probability measures on Abelian metrizable groups [Book]
The rate of escape for random walks on polycyclic and metabelian groups
We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on some abelian-by-cyclic groups via a comparison to the toppling of a dissipative abelian...
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 Resolvent for Simple Random Walks on the Free Product of Two Discrete Groups.
The right tail exponent of the Tracy–Widom distribution
The Tracy–Widom distribution is the large dimensional limit of the top eigenvalue of random matrix ensembles. We use the stochastic Airy operator representation to show that as the tail of the Tracy–Widom distribution satisfies
The spectral laws of Hermitian block-matrices with large random blocks.
The structure of limit measures and their supports on topological semigroups.
The tail -fields of recurrent Markov processes
The Wiener Property for a Class of Discrete Hypergroups.
The Wold-Cramér concordance problem for Banach-space-valued stationary processes
Théorème central limite local sur certains groupes de Lie
Théorème central limite local sur les extensions compactes de
Théorème central limite sur les groupes nilpotents