Nonlinear Parabolic Equations with Cc Adll Ag Noise

We dispense with semimartingale (and Dirichlet process) assumptions while investigating arbitrary-order stochastic semi-linear parabolic equations. The emergence of fractional L evy processes in pressing applications like communication networks and mathematical nance highlights the need for studying stochastic evolutionary equations under general noise conditions. Our principle result states that there exists a unique mild C N-valued solution to dy(t; x) = 2 4 X jmjj2p A m (t; x)@ m x y(t; x) + (t; y(t))(x) 3 5 dt + d t (x)u(t; x) on 0;1) R d that is HH older continuous on average, where f t ; t 0g and fu t ; t 0g are any given processes such that t ! t u t and t ! t 1? 1 2p t @ t u t are D H 1 0; 1)-valued respectively D H 2 0; 1)-valued processes. H 1 ; H 2 are Hilbert spaces of functions deened within. Naturally, due to the full generality allowed for , we will have to specify how to interpret our stochastic integrals and mild solutions. In fact, our purely analytical methods are general enough to allow to be a higher variation process like an iterated Brownian motion. Some novel and technical results on bounds for fundamental solutions to parabolic equations as well as for approximations in some extended Sobolev-like spaces are also given.