  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 can not be satisfied in a straight way. For this, we utilize the
characteristic structure of nonlinear term and refined analysis to overcome
this gap.
