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Existence, Uniqueness and Stability of Mild Solutions for Time-Dependent Stochastic Evolution Equations with Poisson Jumps and Infinite Delay

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Abstract

In this paper, we study a class of time-dependent stochastic evolution equations with Poisson jumps and infinite delay. We establish the existence, uniqueness and stability of mild solutions for these equations under non-Lipschitz condition with Lipschitz condition being considered as a special case. An application to the stochastic nonlinear wave equation, with Poisson jumps and infinite delay, is given to illustrate the obtained theory.

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Authors and Affiliations

  1. Department of Mathematics, Anhui Normal University, Wuhu, 241000, P. R. China

    Y. Ren & L. Chen

  2. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, P. R. China

    Q. Zhou

Authors
  1. Y. Ren
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  2. Q. Zhou
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  3. L. Chen
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Corresponding author

Correspondence to Y. Ren.

Additional information

Communicated by F. Zirilli.

Y. Ren supported by the National Natural Science Foundation of China (Project 10901003), the Great Research Project of Natural Science Foundation of Anhui Provincial Universities (Project KJ2010ZD02) and the Anhui Provincial Natural Science Foundation (Project 10040606Q30).

Q. Zhou supported by the National Natural Science Foundation of China (Projects 11001029 and 10971220) and by the Fundamental Research Funds for the Central Universities (BUPT2009RC0705).

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Ren, Y., Zhou, Q. & Chen, L. Existence, Uniqueness and Stability of Mild Solutions for Time-Dependent Stochastic Evolution Equations with Poisson Jumps and Infinite Delay. J Optim Theory Appl 149, 315–331 (2011). https://doi.org/10.1007/s10957-010-9792-0

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  • DOI: https://doi.org/10.1007/s10957-010-9792-0

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