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This paper is concerned with the problem of asynchronous l2–l∞ filtering for discrete-time stochastic Markov jump systems with sensor nonlinearity. The sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the Bernoulli distribution. A sufficient condition is first given such that the resultant filtering error system, which is a kind of nonhomogeneous Markov jump system, is stochastically stable with a guaranteed l2–l∞ performance index. Then the existence criterion of the desired asynchronous filter with piecewise homogeneous Markov chain is proposed in terms of a set of linear matrix inequalities. A numerical example is given to show the effectiveness and potential of the developed theoretical results.