Some Shannon-McMillan approximation theorems for Markov chain field on the generalized Bethe tree.
Some special cases of a general convergence rate theorem in the law of large numbers.
Sparse recovery with pre-Gaussian random matrices
For an m × N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by ℓ₁-minimization under the optimal condition m ≥ csln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes the ℓ₁-norm and the outer norm depends on probability distributions.
Spectral distribution of the free Jacobi process associated with one projection
Given an orthogonal projection P and a free unitary Brownian motion in a W*-non commutative probability space such that Y and P are *-free in Voiculescu’s sense, we study the spectral distribution νₜ of Jₜ = PYₜPYₜ*P in the compressed space. To this end, we focus on the spectral distribution μₜ of the unitary operator SYₜSYₜ*, S = 2P - 1, whose moments are related to those of Jₜ via a binomial-type expansion already obtained by Demni et al. [Indiana Univ. Math. J. 61 (2012)]. In this connection,...
Spectral properties of large random matrices with independent entries
We consider large Wigner random matrices and related ensembles of real symmetric and Hermitian random matrices. Our results are related to the local spectral properties of these ensembles.
Square variation of Brownian paths in Banach spaces.
Stabile Maße auf Badrikianschen Räumen.
Stabilité du comportement des marches aléatoires sur un groupe localement compact
Dans cet article nous démontrons un théorème de stabilité des probabilités de retour sur un groupe localement compact unimodulaire, séparable et compactement engendré. Nous démontrons que le comportement asymptotique de F*(2n)(e) ne dépend pas de la densité F sous des hypothèses naturelles. A titre d’exemple nous établissons que la probabilité de retour sur une large classe de groupes résolubles se comporte comme exp(−n1/3).
Stability for randomly weighted sums of random elements.
Stability of stochastic optimization problems - nonmeasurable case
This paper deals with stability of stochastic optimization problems in a general setting. Objective function is defined on a metric space and depends on a probability measure which is unknown, but, estimated from empirical observations. We try to derive stability results without precise knowledge of problem structure and without measurability assumption. Moreover, -optimal solutions are considered. The setup is illustrated on consistency of a --estimator in linear regression model.
Stability, sensitivity and sensitivity of characterizations
Stable probability measures on Banach spaces
Stationary measures for random walks in a random environment with random scenery.
Statistical linear spaces. I. Properties of , -topology
Statistiques sur le groupe symétrique
Stochastic antiderivational equations on non-Archimedean Banach spaces.
Stochastic differential equation driven by a pure-birth process
A generalization of the Poisson driven stochastic differential equation is considered. A sufficient condition for asymptotic stability of a discrete time-nonhomogeneous Markov process is proved.
Stochastic processes on totally disconnected topological groups.
Stone-Weierstrass type theorems for large deviations.
Strassen's law of the iterated logarithm
Strassen’s functional form of the law of the iterated logarithm is formulated for partial sums of random variables with values in a strict inductive limit of Frechet spaces of Hilbert space type. The proof depends on obtaining Berry-Essen estimates for Hilbert space valued random variables.