  Consider the following stochastic heat equation, \begin{align*}
\frac{\partial u_t(x)}{\partial t}=-\nu(-\Delta)^{\alpha/2}
u_t(x)+\sigma(u_t(x))\dot{F}(t,\,x), \quad t>0, \; x \in R^d. \end{align*} Here
$-\nu(-\Delta)^{\alpha/2}$ is the fractional Laplacian with $\nu>0$ and $\alpha
\in (0,2]$, $\sigma: R\rightarrow R$ is a globally Lipschitz function, and
$\dot{F}(t,\,x)$ is a Gaussian noise which is white in time and colored in
space. Under some suitable additional conditions, we prove a strong comparison
theorem and explore the effect of the initial data on the spatial asymptotic
properties of the solution. This constitutes an important extension over a
series of recent works.
