This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space L p ( C ) for p>2. We investigate the existence and uniqueness of L p -solution of quantum stochastic differential equations in infinite time horizon by the Burkholder-Gundy inequalities for noncommutative martingales given by Pisier and Xu. Finally, we obtain Markov property and the self-adjointness which is of great significance in the study of optimal control problems. 2020 AMS Subject Classification: 46L51, 47J25, 60H10, 81J25.