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A Stochastic Generalized Ginzburg–Landau Equation Driven by Jump Noise

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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.

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Acknowledgements

LL is supported in part by the NSF from Jiangsu province BK20171029 and the NSF of the Jiangsu Higher Education Committee of China No. 14KJB110016. HG is supported by a China NSF Grant Nos. 11531006, 11771123 and PAPD of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. School of Mathematical Sciences and Jiangsu Provincial Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing, 210023, China

    Lin Lin

  2. School of Mathematical Sciences and Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing Normal University, Nanjing, 210023, China

    Hongjun Gao

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  1. Lin Lin
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  2. Hongjun Gao
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Correspondence to Hongjun Gao.

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Lin, L., Gao, H. A Stochastic Generalized Ginzburg–Landau Equation Driven by Jump Noise. J Theor Probab 32, 460–483 (2019). https://doi.org/10.1007/s10959-017-0806-9

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  • DOI: https://doi.org/10.1007/s10959-017-0806-9

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