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In this paper, we construct and analyze a stochastic predator–prey system where apart from direct predation the prey population is affected by the fear induced from predators. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological interpretation, the existence of a stationary distribution indicates that both the prey and predator species will be persistent and coexistent in the long term. • A stochastic predator–prey system with fear effect is proposed and studied. • Criteria for the existence of a unique ergodic stationary distribution are obtained. • A stationary distribution shows that both the prey and predator species will persist. [ABSTRACT FROM AUTHOR]