Abstract
The final objective of our study is to propose a finite-dimensional approach to systems of parabolic partial differential equations perturbed by low-order noises of Brownian or fractional Brownian type. The present article is the preparatory first part, where we introduce partial pathwise integrals over D and (a, b) × D, where D is a smooth bounded domain in ℝ n . Corresponding stochastic versions appear as limit cases.