LAGRANGIAN FEYNMAN FORMULAS FOR SECOND-ORDER PARABOLIC EQUATIONS IN BOUNDED AND UNBOUNDED DOMAINS

DOI10.1142/S0219025710004097zbMath1204.47096OpenAlexW2095039712WikidataQ125623115 ScholiaQ125623115MaRDI QIDQ3058120

O. G. Smolyanov, Martin Grothaus, Yana Kinderknecht

Publication date: 18 November 2010

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

Full work available at URL: https://doi.org/10.1142/s0219025710004097

zbMATH Keywords

boundary value problemsdiffusion processesFeynman-Kac formulasFeynman formulasapproximations of functional integralsapproximations of transitional densitiesvariable diffusion coefficient

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Markov semigroups and applications to diffusion processes (47D07) Diffusion processes (60J60) Applications of operator theory to differential and integral equations (47N20) Schrödinger and Feynman-Kac semigroups (47D08)

Related Items

Quasi-Feynman formulas -- a method of obtaining the evolution operator for the Schrödinger equation, Smooth Contractive Embeddings and Application to Feynman Formula for Parabolic Equations on Smooth Bounded Domains, Solution of a Cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula, The Method of Chernoff Approximation, Feynman-Kac and Feynman formulas for infinite-dimensional equations with Vladimirov operator, LAGRANGIAN AND HAMILTONIAN FEYNMAN FORMULAE FOR SOME FELLER SEMIGROUPS AND THEIR PERTURBATIONS, Chernoff approximation of subordinate semigroups, Feynman formulae and phase space Feynman path integrals for tau-quantization of some Lévy-Khintchine type Hamilton functions, Formulas that represent Cauchy problem solution for momentum and position Schrödinger equation, Solution-giving formula to Cauchy problem for multidimensional parabolic equation with variable coefficients, Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations, Explicit formula for evolution semigroup for diffusion in Hilbert space, DISCONTINUITY OF FOURIER TRANSFORMS OF POISSONIAN TYPE COUNTABLY ADDITIVE MEASURES, Feynman formulas and path integrals for some evolution semigroups related to \(\tau\)-quantization

Cites Work

• Feynman formula for a class of second-order parabolic equations in a bounded domain
• Chernoff's theorem and discrete time approximations of Brownian motion on manifolds
• Feynman formulas for particles with position-dependent mass
• Parabolic equations and Feynman-Kac formula on general bounded domains
• Surface measures and initial boundary value problems generated by diffusions with drift
• Function integrals corresponding to a solution of the Cauchy-Dirichlet problem for the heat equation in a domain of a Riemannian manifold
• Feynman formulas and functional integrals for diffusion with drift in a domain on a manifold
• The Proof of the Feynman–Kac Formula for Heat Equation on a Compact Riemannian Manifold
• SMOLYANOV–WEIZSÄCKER SURFACE MEASURES GENERATED BY DIFFUSIONS ON THE SET OF TRAJECTORIES IN RIEMANNIAN MANIFOLDS
• Hamiltonian Feynman path integrals via the Chernoff formula
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• An Operator Calculus Having Applications in Quantum Electrodynamics