An application of Ito-Follmer calculus to bilinear rough evolution equations

Abstract

We present an extension of some results connected to the existence of pathwise solutions to bilinear evolution equations in Hilbert spaces that are driven by paths of low regularity. The bilinear problem is closely connected to a certain non-autonomous Cauchy problem and in the article, sufficient conditions for the existence of its solution are given in the parabolic as well asi the hyperbolic case.

Keywords

• Ito-Follmer calculus
• pth-variation along a sequence of partitions
• multiplicative noise
• fractional Brownian motion
• rough paths