Bernstein–Jackson Inequalities on Gaussian Hilbert Spaces
Oleh Lopushansky
Abstract
Abstract Estimates of best approximations by exponential type analytic functions in Gaussian random variables with respect to the Malliavin derivative in the form of Bernstein–Jackson inequalities with exact constants are established. Formulas for constants are expressed through basic parameters of approximation spaces. The relationship between approximation Gaussian Hilbert spaces and classic Besov spaces are shown.
Topics & Concepts
MathematicsExponential typeGaussianHilbert spaceExponential functionPure mathematicsBernstein inequalitiesDerivative (finance)Mathematical analysisConstant (computer programming)InequalityApplied mathematicsPhysicsQuantum mechanicsComputer scienceEconomicsProgramming languageFinancial economicsApproximation Theory and Sequence SpacesAdvanced Harmonic Analysis ResearchMathematical Approximation and Integration