ASYMPTOTICS OF INFINITE-DIMENSIONAL INTEGRALS WITH RESPECT TO SMOOTH MEASURES I

DOI10.1142/S021902579900031XzbMath1043.46507MaRDI QIDQ4810357

Victoria Steblovskaya, Sergio A. Albeverio

Publication date: 3 September 2004

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

Mathematics Subject Classification ID

Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (7)

A class of Lévy driven SDEs and their explicit invariant measures ⋮ Small noise asymptotic expansions for stochastic PDE's driven by dissipative nonlinearity and Lévy noise ⋮ Asymptotic expansions for SDE's with small multiplicative noise ⋮ Generalized Fresnel integrals ⋮ Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables ⋮ 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

• The method of stationary phase for oscillatory integrals on Hilbert spaces
• Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I
• Precise asymptotics of certain Wiener functionals
• On the Morse index in variational calculus
• Uniqueness of Gibbs states for quantum lattice systems
• Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
• Modes and quasimodes
• Methods de laplace et de la phase stationnaire sur l'espace de wiener
• Asymptotic evaluation of certain Markov process expectations for large time—III
• asymptotics of oscillatory integrals with quadratic phase function on wiener space
• Homogeneous Chaos, p-Forms, Scaling and the Feynman Integral
• Oscillatory integrals, lagrange immersions and unfolding of singularities
• The Laplace method for probability measures in Banach spaces
• Analytic functions, Cauchy formula, and stationary phase on a real abstract Wiener space

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