Feynman formulas and functional integrals for diffusion with drift in a domain on a manifold

DOI10.1134/S0001434608030024zbMath1155.58302OpenAlexW1987077243WikidataQ126201656 ScholiaQ126201656MaRDI QIDQ2517979

Yana Kinderknecht

Publication date: 12 January 2009

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434608030024

zbMATH Keywords

path integralRiemannian manifoldWiener measureCauchy-Dirichlet problemfunctional integralFeynman formuladiffusion with driftFeynman-Kac-itô formulaWeizsäcker-smolyanov surface measure

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Applications of manifolds of mappings to the sciences (58D30) Boundary value problems on manifolds (58J32)

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Cites Work

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• Representations of the solution of the Cauchy-Dirichlet problem for the heat equation in a domain of a compact Riemannian manifold by functional integrals
• Wiener surface measures on trajectories in Riemannian manifolds
• Chernoff's theorem and discrete time approximations of Brownian motion on manifolds
• Finite dimensional approximations to Wiener measure and path integral formulas on manifolds
• Diffusion on compact Riemannian manifolds, and surface measures.
• Surface measures on trajectories in Riemannian manifolds generated by diffusions.
• Feynman integrals over trajectories in Riemannian manifolds
• Note on product formulas for operator semigroups
• \(C^1\) isometric imbeddings
• Product formulas, nonlinear semigroups, and addition of unbounded operators
• THE SMOLYANOV SURFACE MEASURE ON TRAJECTORIES IN A RIEMANNIAN MANIFOLD
• Hamiltonian Feynman path integrals via the Chernoff formula
• Feynman Integrals and the Schrödinger Equation

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