Approximation of a class of Wiener integrals

and since evaluation of this integral by analysis often cannot be done, it is of some practical interest to investigate the possibility of numerically evaluating this integral. Such a calculation is expected to require an enormous amount of arithmetic since it involves the evaluation of a fc-fold integral where k >5> 1 ; an exact evaluation requires going to the limit k —* ». Consequently, it is taken for granted that the services of a large computing machine may be required. In this paper we derive an approximation formula for the conditional Wiener integral of the functional Fix) in Eq. ( 1.1 ) that may be useful for machine calculations. The main result is the formula