<abstract> In this paper, we propose and investigate an impulsive stochastic predator-prey Lotka-Volterra model with infinite delay and Lévy jumps. Sufficient criteria for permanence in time average and the threshold between stability in time average and extinction are provided. For the corresponding case without impulse, the easily substantiated sufficient criteria for stability in distribution are derived. Our results demonstrate that, first of all, the coefficients related to infinite delay have some effects on permanence in time average and stability in distribution; then impulsive perturbations play a prominent part in keeping the permanence in time average despite the unfavourable factor Lévy jumps causes. </abstract>
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