Runge-Kutta method for computing Wiener integrals of functionals of exponential type. (Russian) Zbl 0552.65017

Gladyshev, S. A.; Mil’shtejn, G. N.

Zh. Vychisl. Mat. Mat. Fiz. 24, No. 8, 1136-1149 (1984).

A fourth order Runge-Kutta method is given for the evaluation of Wiener integrals \[ (1)J=\int_{C^ n}V(x(\cdot))d_ wx \] of functionals of exponential type \[ V(x(\cdot))=\exp [\int^{T}_{0}f(s,x_ 1(s),...,x_ n(s))ds]. \] The method is based on the continuity of (1) and on a stochastic system of differential equations by Ito.

Reviewer: M.Bartušek

MSC:

65D32	Numerical quadrature and cubature formulas
28C20	Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
41A55	Approximate quadratures
65C99	Probabilistic methods, stochastic differential equations
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

Runge-Kutta method; Wiener integrals; functionals of exponential type; stochastic system of differential equations