Indépendance conditionnelle permutable
Inégalités isopérimétriques en analyse et probabilités
Inégalités isopérimétriques et calcul stochastique
Infinite probabilistic secret sharing
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of participants allows us to investigate their abstract properties, to connect the topic to other branches of mathematics, and to discover new design paradigms. A scheme is perfect if unqualified subsets have no information on the secret, that is, their total share...
Infinite products of random matrices and repeated interaction dynamics
Let Ψn be a product of n independent, identically distributed random matrices M, with the properties that Ψn is bounded in n, and that M has a deterministic (constant) invariant vector. Assume that the probability of M having only the simple eigenvalue 1 on the unit circle does not vanish. We show that Ψn is the sum of a fluctuating and a decaying process. The latter converges to zero almost surely, exponentially fast as n→∞. The fluctuating part converges in Cesaro mean to a limit that is characterized...
Infinitely divisible cylindrical measures on Banach spaces
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Further properties of infinitely divisible cylindrical measures such as continuity are derived. Moreover, the classification result enables us to deduce new results on...
Infinitely divisible measures on the cone of an ordered locally convex vector spaces
Infinitely divisible probability measures and the converse Kolmogorov inequality in Banach spaces
Infinitesimal behaviour of a continuous local martingale
Integrability of seminorms, the 0-1 law and the affine kernel for product measures
Integral Representation in the Set of Solutions of a Generalized Moment Problem.
Integrals related to stationary processes and cylindrical martingales
Integration seperat stetiger Funktionen
Intégration stochastique et géométrie des espaces de Banach
Interlaced processes on the circle
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned...
Invariance principles for random walks conditioned to stay positive
Let {Snbe a random walk in the domain of attraction of a stable law , i.e. there exists a sequence of positive real numbers ( an) such that Sn/anconverges in law to . Our main result is that the rescaled process (S⌊nt⌋/an, t≥0), when conditioned to stay positive, converges in law (in the functional sense) towards the corresponding stable Lévy process conditioned to stay positive. Under some additional assumptions, we also prove a related invariance principle for the random walk killed at its first...
Invariance principles in Hölder spaces.
Isomorphically isometric probabilistic normed linear spaces.
Probabilistic normed linear spaces (briefly PNL spaces) were first studied by A. N. Serstnev in [1]. His definition was motivated by the definition of probabilistic metric spaces (PM spaces) which were introduced by K. Menger and subsequebtly developed by A. Wald, B. Schweizer, A. Sklar and others.In a previuos paper [2] we studied the relationship between two important classes of PM spaces, namely E-spaces and pseudo-metrically generated PM spaces. We showed that a PM space is pseudo-metrically...
Isoperimetric problem for uniform enlargement
We consider an isoperimetric problem for product measures with respect to the uniform enlargement of sets. As an example, we find (asymptotically) extremal sets for the infinite product of the exponential measure.