On two reverse inequalities in the Segal-Bargmann space.
On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions
Let (X,d) be a metric space. Let Φ be a family of real-valued functions defined on X. Sufficient conditions are given for an α(·)-monotone multifunction to be single-valued and continuous on a weakly angle-small set. As an application it is shown that a γ-paraconvex function defined on an open convex subset of a Banach space having separable dual is Fréchet differentiable on a residual set.
One counterexample concerning the Fréchet differentiability of convex functions on closed sets
Opérateurs multiplicativement liés
Operator valued probability theory.
Optimal cubature formulas in a reflexive Banach space
Sequences of cubature formulas with a joint countable set of nodes are studied. Each cubature formula under consideration has only a finite number of nonzero weights. We call a sequence of such kind a multicubature formula. For a given reflexive Banach space it is shown that there is a unique optimal multicubature formula and the sequence of the norm of optimal error functionals is monotonically decreasing to 0 as the number of the formula nodes tends to infinity.
Optimal estimators in learning theory
This paper is a survey of recent results on some problems of supervised learning in the setting formulated by Cucker and Smale. Supervised learning, or learning-from-examples, refers to a process that builds on the base of available data of inputs and outputs , i = 1,...,m, a function that best represents the relation between the inputs x ∈ X and the corresponding outputs y ∈ Y. The goal is to find an estimator on the base of given data that approximates well the regression function of...
Optimal mean-variance bounds on order statistics from families determined by star ordering
We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.
Optimal reinsurance.
Optimal trend estimation in geometric asset price models
In the general geometric asset price model, the asset price P(t) at time t satisfies the relation , t ∈ [0,T], where f is a deterministic trend function, the stochastic process F describes the random fluctuations of the market, α is the trend coefficient, and σ denotes the volatility. The paper examines the problem of optimal trend estimation by utilizing the concept of kernel reproducing Hilbert spaces. It characterizes the class of trend functions with the property that the trend coefficient...
Orbites périodiques de systèmes conservatifs
Orthogonal Forms and Probability in von Neumann Algebras.
Paraconvex analysis
Paraconvex functions and paraconvex sets
We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded. We...
Parameter-elliptic and parabolic pseudodifferential boundary problems in global Lp Sobolev spaces.
Partial Hilbert spaces and amplitude functions
Path integrals in finite sets
Periodic and almost periodic flows of periodic Ito equations
Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the -bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established.
Persistence of Crandall-Rabinowitz type bifurcations under small perturbations.
Phase space properties of local observables and structure of scaling limits