The generalized hu-meyer formula for random kernels

A theory of Hilbert-space-valued traces and multiple integration is developed for kernels inL ²(0, 1]^p × Θ). The multiple Ogawa and the multiple Stratonovich integrals for such kernels are introduced and sufficient conditions for their existence are obtained. The derivation of the Hu-Meyer formula connecting the multiple Ogawa and the multiple Stratonovich integrals requires the introduction of traces of random kernels. Such a derivation is obtained under appropriate conditions. This research was supported by the National Science Foundation and the Air Force Office of Scientific Research Grant No. F49620 92 J 0154 and the Army Research Office Grant No. DAAL03-92-G-0008.