On the convolution of a probability measure.
On the correct discrimination of Gaussian hypotheses. II.
On the decomposition of continuous flows on the Polish space
On the definition of a probalistic normed space.
On the density of log concave seminorms on vector spaces
On the distribution of random variables corresponding to Musielak-Orlicz norms
Given a normalized Orlicz function M we provide an easy formula for a distribution such that, if X is a random variable distributed accordingly and X₁,...,Xₙ are independent copies of X, then , where is a positive constant depending only on p. In case p = 2 we need the function t ↦ tM’(t) - M(t) to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into L₁[0,1]. We also provide a general result replacing the -norm by an arbitrary N-norm. This...
On the distribution of the norm for a gaussian measure
On the existence of conditional density functions
On the existence of probability measures with given marginals
Let be a compact ordered space and let be two probabilities on such that for every increasing continuous function . Then we show that there exists a probability on such that(i) , where is the graph of the order in ,(ii) the projections of onto are and .This theorem is generalized to the completely regular ordered spaces of Nachbin and also to certain infinite products. We show how these theorems are related to certain results of Nachbin, Strassen and Hommel.
On the existence of resolvents
On the Existence of Uniformly Distributed Sequences in Compact Topological Spaces II.
On the existence of uniformly distributed sequences in compact spaces
On the explosion of the local times along lines of brownian sheet
On the Feller strong law of large numbers for fields of -valued random variables.
On the Fourier transform on the infinite symmetric group.
On the generating functional of a convolution semigroup on a Hilbert-Lie group
On the Heyde theorem for discrete Abelian groups
Let X be a countable discrete Abelian group, Aut(X) the set of automorphisms of X, and I(X) the set of idempotent distributions on X. Assume that α₁, α₂, β₁, β₂ ∈ Aut(X) satisfy . Let ξ₁, ξ₂ be independent random variables with values in X and distributions μ₁, μ₂. We prove that the symmetry of the conditional distribution of L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ implies that μ₁, μ₂ ∈ I(X) if and only if the group X contains no elements of order two. This theorem can be considered as an analogue...
On the integrability of Banach space valued Walsh polynomials
On the Integral Representation in Convex Noncompact Sets of Tight Measures.
On the invariant measure of the random difference equation Xn = AnXn−1 + Bn in the critical case
We consider the autoregressive model on ℝd defined by the stochastic recursion Xn = AnXn−1 + Bn, where {(Bn, An)} are i.i.d. random variables valued in ℝd× ℝ+. The critical case, when , was studied by Babillot, Bougerol and Elie, who proved that there exists a unique invariant Radon measureν for the Markov chain {Xn}. In the present paper we prove that the weak limit of properly dilated measure ν exists and defines a homogeneous measure on ℝd ∖ {0}.