Asymptotic expansions for ornstein-uhlenbeck semigroups perturbed by potentials over banach spaces

DOI10.1080/17442500008834240zbMath0973.60064OpenAlexW1967579663MaRDI QIDQ4955493

Victoria Steblovskaya, Haio Röckle, Sergio A. Albeverio

Publication date: 11 July 2001

Published in: Stochastics and Stochastic Reports (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442500008834240

zbMATH Keywords

perturbationasymptotic expansionclassical dynamical systemsinfinite-dimensional Sturm-Liouville probleminfinite-dimensional Wiener integrals

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Asymptotic expansions of solutions to PDEs (35C20) 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)

Related Items (14)

A class of Lévy driven SDEs and their explicit invariant measures ⋮ Asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths ⋮ Laplace approximation for rough differential equation driven by fractional Brownian motion ⋮ Infinite-dimensional stochastic differential equations obtained by subordination and related Dirichlet forms. ⋮ Small noise asymptotic expansions for stochastic PDE's driven by dissipative nonlinearity and Lévy noise ⋮ Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions ⋮ Asymptotic expansions for SDE's with small multiplicative noise ⋮ Generalized Fresnel integrals ⋮ Feynman path integrals for polynomially growing potentials ⋮ Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables ⋮ Ornstein–Uhlenbeck operators and semigroups ⋮ A unified approach to infinite-dimensional integration ⋮ Asymptotics of Gaussian integrals in infinite dimensions ⋮ Small noise asymptotic expansions for stochastic PDE's. I: The case of a dissipative polynomially bounded non linearity

Cites Work

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• Asymptotic analysis of Gaussian integrals. II: Manifold of minimum points
• Gaussian random fields, infinite dimensional Ornstein-Uhlenbeck processes, and symmetric Markov processes
• The method of stationary phase for oscillatory integrals on Hilbert spaces
• Laplace approximations for sums of independent random vectors. II: Degenerate maxima and manifolds of maxima
• Classical Dirichlet forms on topological vector spaces - the construction of the associated diffusion process
• Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I
• Feynman path integrals and the trace formula for the Schrödinger operators
• Precise asymptotics of certain Wiener functionals
• An invariance result for capacities on Wiener space
• Introduction to the theory of (non-symmetric) Dirichlet forms
• On the continuity of Ornstein-Uhlenbeck processes in infinite dimensions
• Gaussian measures in Banach spaces
• On the Schrödinger equation with potentials which are Laplace transforms of measures
• The probabilistic Feynman-Kac formula for an infinite-dimensional Schrödinger equation with exponential and singular potentials
• Banach space-valued Ornstein-Uhlenbeck processes with general drift coefficients
• Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation
• Stochastic differential equations in infinite dimensions: Solutions via Dirichlet forms
• Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
• Note on product formulas for operator semigroups
• Potential theory on Hilbert space
• Transformations of Wiener integrals under translations
• On the Product of Semi-Groups of Operators
• Methods de laplace et de la phase stationnaire sur l'espace de wiener
• Regular fundamental solution for a parabolic equation on an infinite–dimensional space
• Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation
• Non-Symmetric Ornstein-Uhlenbeck Processes in Banach Space Via Dirichlet Forms
• The Laplace method for probability measures in Banach spaces
• Abstract Wiener processes and their reproducing Kernel Hilbert spaces
• Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations
• Stochastic Equations in Infinite Dimensions

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