The Proof of the Feynman–Kac Formula for Heat Equation on a Compact Riemannian Manifold

DOI10.1142/S0219025703001109zbMath1067.58030WikidataQ115245788 ScholiaQ115245788MaRDI QIDQ3043505

O. O. Obrezkov

Publication date: 6 August 2004

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

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Brownian motion (60J65) Diffusion processes and stochastic analysis on manifolds (58J65) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (9)

Representation of solutions of the stochastic Schrödinger equation in the form of a Feynman integral ⋮ Function integrals corresponding to a solution of the Cauchy-Dirichlet problem for the heat equation in a domain of a Riemannian manifold ⋮ An approximation to Wiener measure and quantization of the Hamiltonian on manifolds with non-positive sectional curvature ⋮ LAGRANGIAN AND HAMILTONIAN FEYNMAN FORMULAE FOR SOME FELLER SEMIGROUPS AND THEIR PERTURBATIONS ⋮ LAGRANGIAN FEYNMAN FORMULAS FOR SECOND-ORDER PARABOLIC EQUATIONS IN BOUNDED AND UNBOUNDED DOMAINS ⋮ Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions ⋮ О точности разностной схемы для уравнений Навье - Стокса ⋮ Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations ⋮ Feynman formulas and path integrals for some evolution semigroups related to \(\tau\)-quantization

Cites Work

• Feynman formulas for solutions of the Schrödinger equation on compact Riemannian manifolds

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