The problem of fault detection for two-dimensional (2D) Markov jump systems characterized in the form of Roesser model is considered in this paper. An asynchronous fault detection filter is designed to produce a residual signal. The fault detection filter changes from one mode to another asynchronously with the plant's transitions. More specifically, the filter's mode transitions depend on the plant's mode through some conditional probabilities. Moreover, the transition probabilities of the plant and the conditional probabilities are only partially accessible, which appears more practical in real application systems. Under such a framework, sufficient conditions are developed to ensure the asymptotic mean square stability and (Q, R, S)-mu-dissipativity of the overall fault detection system. The parameters in the fault detection filter are given in terms of solutions of an optimization problem. Finally, some simulations are carried out to demonstrate the validity of the presented design techniques. (C) 2019 Elsevier Ltd. All rights reserved.