Measurability Theorems for Stochastic Extremals

Enclosure Theorems for Extremals of Elliptic Parametric Functionals

In the following paper we study parametric functionals. First we introduce a generalized mean curvature (so called F -mean curvature). This enables us to describe extremals of parametric funcionals as surfaces of prescribed F -mean curvature. Furthermore we give a differential equation for arbitrary immersions generalizing ∆X = HN and apply this equation to surfaces of vanishing and prescribed ...

Three Theorems on the Envelope of Extremals by Marston Morse

Karlin’s Basic Composition Theorems and Stochastic Orderings

Suppose λ,x,ζ traverse the ordered sets Λ, X and Z, respectively and consider the functions f(λ,x,ζ) and g(λ,ζ) satisfying the following conditions, (a) f(λ,x,ζ) > 0 and f is TP2 in each pairs of variables when the third variable is held fixed and (b) g(λ,ζ) is TP2. Then the function h(λ,x) =∫Z f(λ,x,ζ)g(λ,ζ)dµ(ζ), defined on Λ×X is TP2 in (λ,x). The aim of this note is to use a new stochast...

Stochastic separation theorems

The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples where the system works properly. We demonstrate that in (moderately) high dimension this separation could be achieved with probability close to one by linear ...

Quantum forbidden-interval theorems for stochastic resonance

We extend the classical forbidden-interval theorems for a stochastic-resonance noise benefit in a nonlinear system to a quantum-optical communication model and a continuous-variable quantum key distribution model. Each quantum forbidden-interval theorem gives a necessary and sufficient condition that determines whether stochastic resonance occurs in quantum communication of classical messages. ...