Finite dimensional approximations to Wiener measure and path integral formulas on manifolds
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Publication:1296778
DOI10.1006/jfan.1999.3413zbMath0943.58024OpenAlexW2012380373WikidataQ126029977 ScholiaQ126029977MaRDI QIDQ1296778
Bruce K. Driver, Lars Andersson
Publication date: 31 August 2000
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jfan.1999.3413
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Cites Work
- A Poincaré lemma for connection forms
- Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces
- Large deviations and the Malliavin calculus
- A multiflow approximation to diffusions
- On integral transformations associated with a certain Lagrangian - as a prototype of quantization
- Index theorem and equivariant cohomology on the loop space
- Classifications of bundle connection pairs by parallel translation and lassos
- Remarks on convergence of the Feynman path integrals
- Mécanique aléatoire
- On the mollifier approximation for solutions of stochastic differential equations
- Weak limit theorems for stochastic integrals and stochastic differential equations
- Stochastic calculus in manifolds. With an appendix by P.A. Meyer
- A Cameron-Martin type quasi-invariance theorem for Brownian motion on a compact Riemannian manifold
- Gaussian measures in Banach spaces
- The Lie bracket of adapted vector fields on Wiener spaces
- Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus
- Formulae for the derivatives of heat semigroups
- Invariant Sobolev calculus on the free loop space
- On the formulation of the Feynman path integral through broken line paths
- Stochastic Jacobi fields and vector fields induced by varying area on path spaces
- Integration by parts for heat kernel measures revisited
- Loop calculations in quantum-mechanical non-linear sigma models
- YM\(_ 2\): Continuum expectations, lattice convergence, and lassos
- Renormalized differential geometry on path space: Structural equation, curvature
- Twisted sheets
- Towards a Riemannian geometry on the path space over a Riemannian manifold
- Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold
- Theory of connections
- On the relation between ordinary and stochastic differential equations
- Geometry of manifolds of maps
- Riemannsche Hilbertmannigfaltigkeiten. Periodische Geodätische. Mit einem Anhang von H. Karcher
- Feynman's path integral. Definition without limiting procedure
- Integration by parts formulas and dilatation vector fields on elliptic probability spaces
- Morse theory on Hilbert manifolds
- On the convergence of gangolli processes to brownian motion on a manifold
- Approximation for the solutions of stochastic differential equations. i: lp-convergence
- Approximation for the solutions of stochastic differential equations: ii strong convergence
- The central limit problem for geodesic random walks
- Product formulas and numerical algorithms
- Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups
- A note on the central limit theorem for geodesic random walks
- On the construction of certain diffusions on a differentiable manifold
- Space-Time Approach to Non-Relativistic Quantum Mechanics
- A class of integration by parts formulae in stochastic analysis I
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