Consider the following stochastic partial differential equation, \begin{ equation*} \partial_t u_t(x)= \mathcal{ L}u_t(x)+ \sigma (u_t(x))\dot F(t,x)\quad{ t>0}\quad\text{ and}\quad x\in R^d. \end{ equation*} The operator $\mathcal{ L}$ is the generator of a strictly stable process and $\dot F$ is the random forcing term which is assumed to be Gaussian. Under some additional conditions, most notably on $\sigma$ and the initial condition, we show non-existence of global random field solutions. Our results are new and complement earlier works.
Categories: math.PR