We study a minimax state estimation (H∞ estimation) problem where the dynamical system's disturbance is controlled by an adversary, and measurements from the system to the estimator are lost intermittently according to an i.i.d. Bernoulli process. We first obtain a stochastic minimax state estimator (SMSE) and a stochastic Riccati equation (SRE) that depend on the random measurement arrival process. We then show that the H ∞ disturbance attenuation parameter determines the existence of the SMSE. We also analyze the asymptotic behavior of the SRE by showing that the expected value of the SRE is bounded. In particular, we characterize explicit conditions of the disturbance attenuation parameter and the measurement arrival rate above which the expected value of the SRE is bounded. It is also shown that under some conditions, a particular limit of the SMSE is the Kalman filter with intermittent observations but without the disturbance term.