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