Differentiable measures and the Malliavin calculus

DOI10.1007/BF02355450zbMath0929.58015OpenAlexW4206624824MaRDI QIDQ1288049

Vladimir I. Bogachev

Publication date: 10 May 1999

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02355450

zbMATH Keywords

Malliavin calculusinvariant measureslogarithmic derivativesdifferentiable measures

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Stochastic calculus of variations and the Malliavin calculus (60H07) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Research exposition (monographs, survey articles) pertaining to probability theory (60-02) Classical measure theory (28A99)

Related Items (42)

Lagrangian chaos and scalar advection in stochastic fluid mechanics ⋮ Surface measures generated by differentiable measures ⋮ Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations ⋮ Banach manifolds with bounded structure and the Gauss-Ostrogradskii formula ⋮ Logarithmic gradient transformation and chaos expansion of Itô processes ⋮ Existence and a priori estimates for Euclidean Gibbs states ⋮ Asymptotic properties of polynomials in Gaussian random variables ⋮ Differentiability of measures in the sense of Skorokhod and related properties ⋮ Lower estimates for densities of solutions to parabolic equations for measures ⋮ TIGHTNESS OF SOBOLEV CAPACITIES IN INFINITE DIMENSIONAL SPACES ⋮ EXTENSIONS OF H-LIPSCHITZIAN MAPPINGS WITH INFINITE-DIMENSIONAL RANGE ⋮ On extensions of Sobolev functions on the Wiener space ⋮ Besov classes on infinite-dimensional spaces ⋮ Second derivatives of convex functions in the sense of A.\ D.\ Aleksandrov on infinite-dimensional spaces with measure ⋮ Fractional order Sobolev classes on infinite-dimensional spaces ⋮ Laplacian generated by the Gaussian measure and ergodic theorem ⋮ The Radon transform in an infinite-dimensional space with Gaussian measure ⋮ On the distributions of smooth functions on infinite-dimensional spaces with measures ⋮ A note on the Malliavin-Sobolev spaces ⋮ Quasi-invariance under flows generated by non-linear PDEs ⋮ Realization of Virasoro unitarizing measures on the set of Jordan curves. ⋮ Absolute continuity and convergence in variation for distributions of functionals of Poisson point measure ⋮ Modeling the topology of a dynamical network via Wiener filtering approach ⋮ On closability of classical Dirichlet forms. ⋮ A condition for the positivity of the density of an invariant measure ⋮ A priori estimates for symmetrizing measures and their applications to Gibbs states ⋮ Fractional smoothness of images of logarithmically concave measures under polynomials ⋮ Sobolev functions on infinite-dimensional domains ⋮ Laplacian with respect to a measure on a Hilbert space and an \(L_2\)-version of the Dirichlet problem for the Poisson equation ⋮ The Radon transform in infinite-dimensional spaces ⋮ Uniqueness of weighted Sobolev spaces with weakly differentiable weights ⋮ The Dirichlet problem with Laplacian with respect to a measure in the Hilbert space ⋮ On uniqueness of invariant measures for finite- and infinite-dimensional diffusions ⋮ Furstenberg transformations on Cartesian products of infinite-dimensional tori ⋮ Exponential ergodicity of the solutions to SDE's with a jump noise ⋮ Construction of non-Gaussian surface measures by Malliavin's method ⋮ A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations ⋮ Absolutely continuous flows generated by Sobolev class vector fields in finite and infinite dimensions ⋮ Comparison of two definitions of Besov classes on infinite-dimensional spaces ⋮ On existence of a solution for differential equation with interaction ⋮ Surface measures and tightness of \((r,p)\)-capacities on Poisson space ⋮ Mosco convergence of Dirichlet forms in infinite dimensions with changing reference measures

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• [https://portal.mardi4nfdi.de/wiki/Publication:3889862 Martingales, the Malliavin calculus and hypoellipticity under general H�rmander's conditions]

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