A new algorithm and worst case complexity for Feynman-Kac path integration.

DOI10.1006/jcph.2000.6599zbMath1052.81520OpenAlexW2033791986MaRDI QIDQ5926791

Grzegorz W. Wasilkowski, Leszek Plaskota, Henryk Woźniakowski

Publication date: 2000

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.2000.6599

zbMATH Keywords

multivariate approximationWiener measure

Mathematics Subject Classification ID

Computational methods for problems pertaining to quantum theory (81-08) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30)

Related Items (20)

Worst case complexity of multivariate Feynman--Kac path integration ⋮ Liberating the Dimension for Function Approximation and Integration ⋮ Liberating the dimension for \(L_2\)-approximation ⋮ On tractability of linear tensor product problems for \(\infty \)-variate classes of functions ⋮ Tractability of approximation of \(\infty\)-variate functions with bounded mixed partial derivatives ⋮ Tractability of infinite-dimensional integration in the worst case and randomized settings ⋮ On sub-polynomial lower error bounds for quadrature of SDEs with bounded smooth coefficients ⋮ Efficient algorithms for multivariate and \(\infty\)-variate integration with exponential weight ⋮ On the complexity of computing quadrature formulas for marginal distributions of SDEs ⋮ Average case tractability of approximating ∞-variate functions ⋮ The randomized information complexity of elliptic PDE ⋮ On the complexity of parabolic initial-value problems with variable drift ⋮ Infinite-dimensional integration and the multivariate decomposition method ⋮ Liberating the dimension ⋮ A path integration formulation of stochastic-Lagrangian models of turbulent flow ⋮ Hyperbolic cross approximation in infinite dimensions ⋮ Applying reproducing kernels to the evaluation and approximation of the simple and time-dependent imaginary time harmonic oscillator path integrals ⋮ Infinite-dimensional integration on weighted Hilbert spaces ⋮ Quadrature formulas for the Wiener measure ⋮ An optimal Monte Carlo algorithm for multivariate Feynman–Kac path integrals

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• On the power of adaption
• A ``Simpson's rule for the numerical evaluation of Wiener's integrals in function space
• On tractability of path integration
• Approximation of a Class of Wiener Integrals
• Accurate Evaluation of Wiener Integrals
• On Distributions of Certain Wiener Functionals
• Theory of Reproducing Kernels

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