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A note on the neutral stochastic functional differential equation with infinite delay and Poisson jumps in an abstract space. (English) Zbl 1223.34110

Summary: We prove the existence and uniqueness of the solution to neutral stochastic functional differential equation with infinite delay and Poisson jumps in the phase space \(\mathfrak B\) with non-Lipschitz coefficients. The known results that appeared in the studies by Y. Ren and N. Xia [Appl. Math. Comput. 210, No. 1, 72–79 (2009; Zbl 1167.34389); Appl. Math. Comput. 214, No. 2, 457–461 (2009; Zbl 1221.34222)] and Y. Xu and S. Hu [Acta Appl. Math. 110, No. 2, 627–638 (2010; Zbl 1194.34151)] are generalized and improved. An example is provided to illustrate the theory.{
©2009 American Institute of Physics}

MSC:

34K50 Stochastic functional-differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K40 Neutral functional-differential equations
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