Instantaneous blowup for interacting SDEs with superlinear drift

We consider a system of interacting SDEs on the integer lattice with multiplicative noise and a drift satisfying the finite Osgood's condition. We show instantaneous everywhere blowup for initial profiles decaying slower than $\exp \left( -\sqrt{\big|\log |x|\big|}\right)$. We employ the splitting-up method to compare the interacting system to a one-dimensional SDE which blows up.

No reviews yet.

No comments yet.