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In this paper, the asynchronous H∞ filtering problem for discrete-time Markov jump neural networks is investigated.Since the information on the jump mode of the neural networks is not always available, the mode of the filter often doesnt correspond to that of the discrete-time Markov jump neural networks.To overcome this kind of asynchronous phenomenon, a novel filtering design method is proposed.Here the mode of the neural networks and the mode of the filter are subject to two different Markov chains.By introducing a unified Lyapunov functional, we derive a sufficient condition in terms of linear matrix inequality(LMI) such that the resultant filtering error system is stochastically stable.Finally a numerical example is given to demonstrate the effectiveness of the proposed theoretical results.