  We consider stochastic equations of the prototype $du(t,x) =(\Delta
u(t,x)+u(t,x)^{1+\beta})dt+\kappa u(t,x) dW_{t}$ on a smooth domain $D\subset
\mathord{\rm I\mkern-3.6mu R\:}^d$, with Dirichlet boundary condition, where
$\beta$, $\kappa$ are positive constants and $\{W_t $, $t\ge0\}$ is a
one-dimensional standard Wiener process. We estimate the probability of finite
time blowup of positive solutions, as well as the probability of existence of
non-trivial positive global solutions.
