On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with   L\'{e}vy noise
  In this article we deal with stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasise is on analysing the effect of multiplicative L\'{e}vy noise to such problems and establishing wellposedness by developing a suitable weak entropy solution framework. The proof of existence is based on the vanishing viscosity technique. The uniqueness is settled by interpreting Kruzkov's doubling technique in the presence noise. 
Imran H. Biswas, Ananta K. Majee, Guy Vallet
math.AP