Stochastic Reaction-Diffusion Systems With Hölder Continuous Multiplicative Noise
Stochastic Reaction-Diffusion Systems With Hölder Continuous Multiplicative Noise
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.