Bulletin of the
Korean Mathematical Society BKMS

We derive a comparison theorem for solutions of the following stochastic partial differential equations in a Hilbert space $H.$ $$Lu^i=\a(u^i) \dot M(t,x)+\beta^i(u^i),\,\,\text{for }i=1,2,$$ where $Lu^i=\frac{\partial u^i}{\partial t} -Au^i,$ $A$ is a linear closed operator on $H$ and $ \dot M(t,x)$ is a spatially homogeneous Gaussian noise with covariance of a certain form. We are going to show that if $\beta^1\le \beta^2$ then $u^1\le u^2$ under some conditions.

Keywords: comparison theorem, SPDE, martingale measure

MSC numbers: 60H15, 35R60, 35R45