A Stochastic Generalized Ginzburg-Landau Equation Driven by Jump Noise

This paper is concerned with the stochastic generalized Ginzburg–Landau equation driven by a multiplicative noise of jump type. By a prior estimate, weak convergence and monotonicity technique, we prove the existence and uniqueness of the solution of an initial-boundary value problem with homogeneous Dirichlet boundary condition. However, for the generalized Ginzburg–Landau equation, such a locally monotonic condition of the nonlinear term cannot be satisfied in a straightforward way. For this, we utilize the characteristic structure of the nonlinear term and refined analysis to overcome this gap.