Gaussian measures on linear spaces

DOI10.1007/BF02362918zbMath0881.28009OpenAlexW2019780789MaRDI QIDQ1920991

Vladimir I. Bogachev

Publication date: 17 February 1998

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

Full work available at URL: https://doi.org/10.1007/bf02362918

zbMATH Keywords

locally convex spacesGaussian measuresRadon measuresMalliavin Calculus

Mathematics Subject Classification ID

Stochastic calculus of variations and the Malliavin calculus (60H07) Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Probability theory on linear topological spaces (60B11)

Related Items (3)

Exploring a Fourier-Malliavin numerical model ⋮ Continuous transforms of a Lebesgue measure. ⋮ Differentiable measures and the Malliavin calculus

Cites Work

• Absolue continuité de probabilités de transition par rapport à une mesure gaussienne dans un espace de Hilbert. (Absolute continuity of transition probabilities with respect to a Gaussian measure in a Hilbert space)
• Processus sur l'espace de Wiener associés à des opérateurs élliptiques à coefficients dans certains espaces de Sobolev. (Processes on the Wiener space associated to elliptic operators with coefficients in certain Sobolev spaces)
• Equations différentielles sur l'espace de Wiener et formules de Cameron- Martin non-linéaires
• Regularity of Gaussian processes
• Integration on loop groups. I: Quasi invariant measures
• Anticipative Girsanov transformations
• Uniform convexity and the distribution of the norm for a Gaussian measure
• Equivalence and perpendicularity of Gaussian processes
• Likelihood ratios of Gaussian processes
• The Gross-Sazonov theorem for signed cylindrical measures
• Intégrales oscillantes stochastiques: Estimation asymptotique de fonctionnelles caractéristiques
• Large deviations and the Malliavin calculus
• On the distribution of the norm for a Gaussian measure
• Lectures on stochastic differential equations and Malliavin calculus
• Capacitary inequalities of the Brunn-Minkowski type
• Unicité de solutions d'équations différentielles sur l'espace de Wiener
• Analysis on Wiener spaces. I: Nonlinear maps
• Onsager-Machlup functionals and maximum a posteriori estimation for a class of non-Gaussian random fields
• Hausdorff measures on the Wiener space.
• On independence and conditioning on Wiener space
• On the Onsager-Machlup functional of diffusion processes around non \(C^ 2\) curves
• Continuity of \(\ell ^ 2\)-valued Ornstein-Uhlenbeck processes
• Sur la régularité de certaines fonctions aléatoires d'Ornstein- Uhlenbeck. (On the regularity of certain Ornstein-Uhlenbeck random processes)
• Differentiability of Lipschitz functions on Banach spaces
• Laplace-Gauß integrals, Gaussian measure asymptotic behaviour and probabilities of moderate deviations
• Three problems of Aronszajn in measure theory
• Negligible sets in locally convex spaces
• Sobolev spaces of Wiener functionals and Malliavin's calculus
• Régularité des mesures et perturbations stochastiques de champs de vecteurs sur des espaces de dimension infinie (Regularity of measures and stochastic perturbations of vector fields on infinite-dimensional spaces)
• Éléments extrémaux pour les inégalités de Brunn-Minkowski gaussiennes (Extreme elements for the Gaussian Brunn-Minkowski inequalities)
• On the rate of convergence in the central limit theorem in Banach spaces
• Generalized stochastic integrals and the Malliavin calculus
• Time reversal of infinite-dimensional diffusions
• The asymmetry indices of stable measures
• Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels
• On (r,p)-capacities for Markov processes
• Existence of invariant measures of diffusions on an abstract Wiener space
• Small tails for the supremum of a Gaussian process
• Traces of harmonic functions and a new path space for the free quantum field
• Degree theory for Wiener maps
• Espaces de Sobolev gaussiens. (Gaussian Sobolev spaces)
• Locally convex spaces with the property of central limit theorem and measure supports
• Exponential integrability of sub-Gaussian vectors
• Absolute continuity of probability laws of Wiener functionals
• On the lower tail of Gaussian seminorms
• A Gaussian measure on \(l^\infty\)
• Normal approximation - some recent advances
• The Malliavin calculus, a functional analytic approach
• Derivatives of Wiener functionals and absolute continuity of induced measures
• L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel
• Hitting probability of a Gaussian vector with values in a Hilbert space in a sphere of small radius
• Laplace's method for Gaussian integrals with an application to statistical mechanics
• Gaussian measure of large balls in \(l_ p^ 1\)
• Precise asymptotics of certain Wiener functionals
• Various topologies in the Wiener space and Lévy's stochastic area
• An invariance result for capacities on Wiener space
• Dirichlet forms and analysis on Wiener space
• Traces of random variables on Wiener space and the Onsager-Machlup functional
• A note on conditional exponential moments and Onsager-Machlup functionals
• When does the Ramer formula look like the Girsanov formula?
• On the continuity of Ornstein-Uhlenbeck processes in infinite dimensions
• Transformation of Wiener measure under anticipative flows
• A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
• Some results of probability measures on linear topological vector spaces with an application to Strassen's log log law
• Non-anticipative representations of equivalent Gaussian processes
• The Ornstein-Uhlenbeck semigroup in an infinite dimensional L\(^2\) setting
• Convex measures on locally convex spaces
• Gaussian measures in Banach spaces
• Geometry of Banach spaces. Selected topics
• Absolute continuity for abstract Wiener spaces
• On Gross differentiation on Banach spaces
• Smooth functions on Banach spaces
• Exponential inequalities for sums of random vectors
• Subgroups of paths and reproducing kernels
• Measurable norms and some Banach space valued Gaussian processes
• Gaussian characterizations of certain Banach spaces
• Every Hilbert subspace of a Wiener space has measure zero
• The Onsager-Machlup function as Lagrangian for the most probable path of a diffusion process
• Gaussian null sets and differentiability of Lipschitz map on Banach spaces
• Quantum mechanical Wiener processes
• Nonlinear transformations on the Wiener space
• Gaussian linear operators
• A characterization of Gibbs measures on \(C(0,1)^{\mathbb{Z}^ d}\) by the stochastic calculus of variations
• Tail probabilities of Gaussian suprema and Laplace transform
• The Gaussian measure of shifted balls
• A conditional approach to the anticipating Girsanov transformation
• Fractional order Sobolev spaces on Wiener space
• Onsager Machlup functionals for non trace class SPDE's
• A large deviation principle for \((r,p)\)-capacities on the Wiener space
• Applications of the degree theorem to absolute continuity on Wiener space
• Nonlinear transformations of the canonical Gauss measure on Hilbert space and absolute continuity
• Exact behavior of Gaussian measures of translated balls in Hilbert spaces
• A property of distributions of diffusion processes
• Gaussian samples approach ``smooth points slowest
• Logarithmic Sobolev inequalities and exponential integrability
• The Onsager-Machlup functions for Gaussian measures
• On the structure of independence on Wiener space
• Positive generalized Wiener functions and potential theory over abstract Wiener spaces
• On a characterization of the Sobolev spaces over an abstract Wiener space
• Characteristic functional of a probability measure absolutely continuous with respect to a Gaussian Radon measure
• Multiple Wiener-Ito integrals possessing a continuous extension
• Negligible sets and differentiable measures in Banach spaces
• On nonlinear transformations of Gaussian measures
• Mesures cylindriques, espaces de Wiener et fonctions aléatoires gaussiennes
• Sard's theorem for hyper-Gevrey functionals on the Wiener space
• Regularity of invariant measures on finite and infinite dimensional spaces and applications
• Some remarks on quasi-invariant actions of loop groups and the group of diffeomorphisms of the circle
• Some remarks on Rademacher's theorem in infinite dimensions
• Generalized Mehler semigroups and applications
• The free Markoff field
• Questions liées à la théorie des espaces de Wiener
• Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms
• The probability of small Gaussian ellipsoids and associated conditional moments
• Rademacher's theorem for Wiener functionals
• Refinement in terms of capacities of certain limit theorems on an abstract Wiener space
• Gaussian measures in function space
• A divergence theorem for Gaussian stochastic process expectations
• Potential theory on Hilbert space
• Processus linéaires, processus généralisés
• A fundamental solution of the parabolic equation on Hilbert space
• Representation of Gaussian processes equivalent to Wiener process
• Abstract Wiener spaces and applications to analysis
• The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
• Gaussian measures on a Banach space
• Measurable linear manifolds in products of linear spaces with measure
• Séminaire sur les fonctions aléatoires linéaires et les mesures cylindriques
• Some regularity properties of diffusion processes on abstract Wiener space
• Linear sample spaces and stable processes
• Sample functions of the Gaussian process
• Some zero-one laws for Gaussian processes
• Régularité de fonctions aléatoires gaussiennes à valeurs vectorielles. (Regularity of Gaussian random functions with vector values)
• Fonctions aléatoires à valeurs dans les espaces lusiniens. (Random functions with values in Lusin spaces)
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• On equivalence of infinite product measures
• Additive functionals on a space of continuous functions. II
• Harmonic analysis and Wiener integrals
• Continuous Markov processes and stochastic equations
• The translation pathology of Wiener space
• Transformations of Wiener integrals under translations
• FUNCTIONALS OF RANDOM PROCESSES AND INFINITE-DIMENSIONAL OSCILLATORY INTEGRALS CONNECTED WITH THEM
• On the Smoothness of Distributions of Functionals of Random Processes
• Mathematical methods of non-Archimedean physics
• On Distributions of Multiple Wiener–ITô Integrals
• A Zero-One Law for Gaussian Processes
• Geometry and probability in Banach spaces
• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• Les fonctions aléatoires comme éléments aléatoires dans les espace de Banach
• Tensor Algebras Over Hilbert Spaces. I
• INTEGRATION OVER HILBERT SPACE AND OUTER EXTENSIONS
• On a property of normal distributions of any stochastic process
• Integration and Nonlinear Transformations In Hilbert Space
• A Family of Integrals Serving to Connect the Wiener and Feynman Integrals
• Distributions in Hilbert Space and Canonical Systems of Operators
• On Transforming a Certain Class of Stochastic Processes by Absolutely Continuous Substitution of Measures
• Sur l’intégrabilité des vecteurs gaussiens
• [https://portal.mardi4nfdi.de/wiki/Publication:3322909 Sur la convergence �troite des mesures gaussiennes]
• Asymptotics for the polaron
• Stochastic differential geometry
• Symétrisation dans l'espace de Gauss.
• Analytic properties of infinite-dimensional distributions
• A Geometrical Approach to Maximum Likelihood Estimation for Infinite-Dimensional Gaussian Location. I
• Two Types of Zero-One Law for a Gaussian Probability
• Supports of Probability Measures in Separable Banach Spaces
• (r, p)-Capacity on the Wiener space and properties of Brownian motion
• Pettis integral and measure theory
• Optimization and nonsmooth analysis
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• SOME RESULTS ON DIFFERENTIABLE MEASURES
• On the Distribution of the Maximum of a Gaussian Process
• A maximal inequality for stochastic convolution integrals on hilbert spaces and space-time regularity of linear stochastic partial differential equations
• THE NEWTON-LEIBNIZ FORMULA ON BANACH SPACES AND APPROXIMATION OF FUNCTIONS OF AN INFINITE-DIMENSIONAL ARGUMENT
• Stochastic Integrals and Differential Measures
• Differentiation Theorem for Gaussian Measures on Hilbert Space
• Functional superanalysis
• Methods de laplace et de la phase stationnaire sur l'espace de wiener
• The role of the Onsager–Machlup Lagrangian in the theory of stationary diffusion process
• Covariance Operators of Probability Measures in Locally Convex Spaces
• Differentiability of Measures Associated with Parabolic Equations on Infinite Dimensional Spaces
• The τ-régularity of Gaussian measures
• Wiener processes on manifolds of maps
• Continuité et différentiabilité des translations dans un espace Gaussien.
• On stability of probability laws with univariate stable marginals
• Mesures Gaussiennes sur un espace localement convexe
• Analyticity of Gaussian Measures
• Non-stable laws with all projections stable
• Fourier Analysis on Linear Metric Spaces
• The Support of Gaussian Measures on Banach Spaces
• Zero-One Laws for Stable Measures
• Mappings of Gaussian Cylindrical Measures in Banach Spaces
• A Note on Uniform Convergence of Stochastic Processes
• Logarithmic Sobolev Inequalities
• On a Formula From the Theory of Gaussian Measures and on the Estimation of Stochastic Integrals
• Asymptotic evaluation of certain markov process expectations for large time, I
• On a Generalization of a Stochastic Integral
• Gaussian radon measures on locally convex spaces.
• Lois e(?) dans les espaces vectoriels et lois stables
• Differentiability of Lipschitzian mappings between Banach spaces
• Dirichlet forms and diffusion processes on rigged Hilbert spaces
• The Density of the Distribution of the Maximum of a Gaussian Process
• Random linear functionals and random integrals
• Proprietes locales d'espaces de type sobolev en dimension
• MEASURES ON LINEAR TOPOLOGICAL SPACES
• Integrability of seminorms, the 0-1 law and the affine kernel for product measures
• Propriété de trace en dimension infinie d'espaces du type Sobolev
• POLYNOMIALS IN LINEAR RANDOM FUNCTIONS
• Gaussian Measures on Function Spaces
• Gaussian Measure of Large Balls in a Hilbert Space
• A Note on Gaussian Measure of Balls in Banach Spaces
• On Adding Independent Stochastic Processes
• Differentiable functions on certain Banach spaces
• An invariance principle for the law of the iterated logarithm
• Linear transformation of a functional integral, II
• Holder Conditions for Realizations of Gaussian Processes
• Differentiable functions with bounded nonempty support on Banach spaces
• Radon-Nikodym Derivatives of Gaussian Measures
• On the Sample Functions of Processes which Can be Added to a Gaussian Process
• On Gaussian Measures Equivalent to Wiener Measure II.
• Some Asymptotic Formulas for Wiener Integrals
• The Radon-Nikodym Theorem for the Bochner Integral
• Equivalent Gaussian Measures with a Particularly Simple Radon-Nikodym Derivative
• Gaussian Measure on a Banach Space and Abstract Winer Measure
• On Some Measures Analogous to Haar Measure.
• A Fundamental Solution of the Parabolic Equation on Hilbert Space. II: The Semigroup Property
• On Gaussian Measures Equivalent to Wiener Measure
• Quasi-Differentiable Functions on Banach Spaces
• A Divergence Theorem for Hilbert Space
• Norm Convergent Expansions for Gaussian Processes in Banach Spaces
• Polynomials and multilinear mappings in topological vector-spaces
• An elementary proof of the Gaussian dichotomy theorem
• Integration Theory on Infinite-Dimensional Manifolds
• Expansions of Vectors in a Banach Space Related to Gaussian Measures
• Absolute Continuity and Radon-Nikodym Derivatives for Certain Measures Relative to Wiener Measure
• Equivalence-Singularity Dichotomies from Zero-One Laws
• On the Oscillation Functions of Gaussian Processes.
• Zero-one laws for Gaussian processes
• Log log law for Gaussian processes
• Non-Hilbertian structure of the Wiener measure
• The Structure of Radon-Nikodym Derivatives with Respect to Wiener and Related Measures
• Oscillation Function of a Multiparameter Gaussian Process
• Subgroups of Sequences and Paths
• On the Density of One Gaussian Measure with Respect to Another
• Integrals devised for special purposes
• Likelihood Ratios for Diffusion Processes With Shifted Mean Values
• The behavior of measure and measurability under change of scale in Wiener space
• Theory of Reproducing Kernels
• Additive Functionals on a Space of Continuous Functions. I
• Notes on Wiener integrals
• Nonlinear Transformations of Volterra Type in Wiener Space
• Fluctuations and Irreversible Processes
• The Wiener Measure of Hilbert Neighborhoods in the Space of Real Continuous Functions
• Transformations of Wiener Integrals Under a General Class of Linear Transformations
• Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations
• Bad rates of convergence for the central limit theorem in Hilbert space
• Stochastic evolution equations
• Stochastic processes and statistical inference
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