We consider nonlinear parabolic stochastic equations of the form ∂tu =
Lu + λσ(u) ˙ξ on the ball B(0, R), where ˙ξ denotes some Gaussian noise and σ
is Lipschitz continuous. Here L corresponds to a symmetric α-stable process killed
upon exiting B(0, R). We will consider two types of noises: space-time white noise
and spatially correlated noise. Under a linear growth condition on σ, we study growth
properties of the second moment of the solutions. Our results are significant extensions
of those in Foondun and Joseph (Stoch Process Appl, 2014) and complement those of
Khoshnevisan and Kim (Proc AMS, 2013, Ann Probab, 2014)
