Neutral stochastic functional differential equations with Levy jumps under the local Lipschitz condition

Mao, Wei and Hu, Liangjian and Mao, Xuerong (2017) Neutral stochastic functional differential equations with Levy jumps under the local Lipschitz condition. Advances in Difference Equations, 57. pp. 1-24. ISSN 1687-1847

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    Abstract

    In this paper, a general neutral stochastic functional differential equations with infinite delay and Lévy jumps (NSFDEwLJs) is studied. We investigate the existence and uniqueness of solutions to NSFDEwLJs at the phase space Cg under the local Carathéodory type conditions. Meanwhile, we also give the exponential estimates and almost surely asymptotic estimates of solutions to NSFDEwLJs.