This paper investigates the problem of H_ index for stochastic linear continuous-time systems involving Markov jump and multiplicative noise. A set of generalized differential Riccati equations (GDREs) are presented and it is shown that the solvability of GDREs is necessary and sufficient for the feasibility of an H_index larger than gamma > 0. Our results extend the corresponding deterministic cases to stochastic systems. Furthermore, the infinite horizon H_ index problem for square systems is considered. Finally, the effectiveness of the obtained results is tested by two examples. (C) 2019 Elsevier Ltd. All rights reserved.