NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS OF HYPERBOLIC TYPE DRIVEN BY LEVY-TYPE NOISES

We study a class of abstract nonlinear stochastic equations of hyperbolic type driven by jump noises, which covers both beam equations with nonlocal, nonlinear terms and nonlinear wave equations. We derive an It (o) over cap formula for the local mild solution which plays an important role in the proof of our main results. Under appropriate conditions, we prove the non-explosion and the asymptotic stability of the mild solution.