A Note on Random Functions
Commun. Korean Math. Soc. 2000 Vol. 15, No. 4, 715-721
Bum Il Hong, Sung Hee Choi, Nahmwoo Hahm
Kyung Hee University, Sun Moon University, Inchon University
Abstract : It is known that one can generate functions distributed according to $r$-fold Wiener measure. So we could estimate the average case errors in a similar way as in Monte-Carlo method. Hence we study the basic properties of the generator of random functions. In addition, because the $r$-fold Wiener process is truly infinitely dimensional and a computer can only handle finitely dimensional spaces, we study in this paper, the properties of generator for an m-dimensional approximation of the $r$-fold Wiener process.
Keywords : Simpson's quadrature, Wiener measure
MSC numbers : 65D30, 28C20
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