PATHWISE SOLUTIONS TO STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
Kening Lu, Orn Schmalfuss · arXiv (Cornell University) · 2012
Combining fractional calculus and the Rough Path Theory we study the existence and uniqueness of mild solutions to evolutions equations driven by a Holder continuous function with Holder exponent in (1/3,1/2). This theory will be the foundation for establishing that infinite-dimensional white-noise-driven evolution equations with non-trivial diffusion coefficientsgenerate random dynamical systems, a problem which has remained open during the last decades.