Stochastic Reaction-Diffusion Systems With Hölder Continuous Multiplicative Noise
Markus Kunze · Stochastic Analysis and Applications · 2015
We prove pathwise uniqueness and strong existence of solutions for stochastic reaction-diffusion systems with a locally Lipschitz continuous reaction term of polynomial growth and Hölder continuous multiplicative noise. Under additional assumptions on the coefficients, we also prove positivity of the solutions.