A Stochastic Generalized Ginzburg–Landau Equation Driven by Jump Noise

Lin Lin () and Hongjun Gao ()
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Lin Lin: Nanjing Normal University
Hongjun Gao: Nanjing Normal University

Journal of Theoretical Probability, 2019, vol. 32, issue 1, 460-483

Abstract: Abstract 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.

Keywords: Stochastic generalized Ginzburg–Landau equation; Jump noise; Existence and uniqueness; 60H15; 35Q99 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-017-0806-9

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