Gradient-type noises I–partial and hybrid integrals

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.

Keywords:

• stochastic partial differential equations
• fractional Brownian sheet
• fractional calculus
• function spaces
• Stieltjes integrals

AMS Subject Classifications::

• 26A33
• 26A42
• 60H05
• 60H15