Computation of conditional Wiener integrals by the composite approximation formulas with weight

摘要

New approximation formulas with weight for the functional integrals with conditional Wiener measure are derived. The formulas are exact on a class of polynomial functionals of a given degree. The convergence of approximations to the exact value of the integral is proved, the estimate of the remainder is obtained. The results are illustrated with numerical examples. The advantages of the formulas over lattice Monte Carlo method are demonstrated in computation of some quantities in Euclidean quantum mechanics.