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

Y. Ren (), Q. Zhou () and L. Chen
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Y. Ren: Anhui Normal University
Q. Zhou: Beijing University of Posts and Telecommunications
L. Chen: Anhui Normal University

Journal of Optimization Theory and Applications, 2011, vol. 149, issue 2, No 5, 315-331

Abstract: 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.

Keywords: Stochastic evolution equation; Evolution operator; Poisson point process; Successive approximation (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-010-9792-0

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