In this paper, we discuss the H_ index problem for stochastic linear discrete-time systems subject to Markovian jump and multiplicative noise, for which, a necessary and sufficient condition for an H_ index larger than gamma > 0 is given in finite time horizon. It is shown that the H_ index larger than a given value is equivalent to the solvability of a certain generalized difference Riccati equation (GDRE). What we have obtained generalizes the results of deterministic systems to stochastic models. Moreover, the H_ index problem for square systems in infinite horizon is also studied. Finally, some examples are presented to illustrate the effectiveness of the proposed theoretical results. (C) 2017 Elsevier Ltd. All rights reserved.