SMOOTH PROBABILITY MEASURES AND ASSOCIATED DIFFERENTIAL OPERATORS

DOI10.1142/S0219025799000047zbMath0936.60052OpenAlexW1982964769MaRDI QIDQ4269407

O. G. Smolyanov, Heinrich von Weizsäcker

Publication date: 29 November 1999

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025799000047

zbMATH Keywords

differential operatorsMalliavin's calculusdifferentiation of measureprobability measures on locally convex space

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Continuity and singularity of induced measures (60G30)

Related Items (17)

Quantum anomalies and logarithmic derivatives of Feynman pseudomeasures ⋮ Change of variable formulas for integrals over superspaces ⋮ Hamiltonian Feynman integrals for equations with the Vladimirov operator ⋮ Absolute Continuity under Time Shift of Trajectories and Related Stochastic Calculus ⋮ Wigner measures on infinite-dimensional spaces and the Bogolyubov equations for quantum systems ⋮ Hamiltonian functional integrals representing regularized traces of higher-order differential operators ⋮ Distributions and analytical measures on infinite-dimensional spaces ⋮ Hamiltonian approach to secondary quantization ⋮ Analytic continuation of the change of variable formula for smooth measures ⋮ A version of the Hörmander–Malliavin theorem in 2-smooth Banach spaces ⋮ Bogolyubov transformations in Wiener-Segal-Fock space ⋮ Generalized Wiener-Segal-Fock representations and Feynman formulae ⋮ О точности разностной схемы для уравнений Навье - Стокса ⋮ NON-SELF-ADJOINT EXTENSIONS OF THE LÉVY–LAPLACIAN AND THE LÉVY–LAPLACE EQUATION ⋮ Family of measures on a space of curves that are quasi-invariant with respect to some action of diffeomorphisms group ⋮ Change of variable formulas for Feynman pseudomeasures ⋮ Transformations of measures via their generalized densities

Cites Work

• The Malliavin calculus, a functional analytic approach
• L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel
• Differentiable families of measures
• Integration by parts on Wiener space and the existence of occupation densities
• [https://portal.mardi4nfdi.de/wiki/Publication:3889862 Martingales, the Malliavin calculus and hypoellipticity under general H�rmander's conditions]
• Formulae with logarithmic derivatives of measures related to the quantization of infinite-dimensional Hamiltonian systems

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