restriction is also needed in this paper. We consider a probabilistic model and the attacker can only partially affect the occurrence probability of a transmission failure. We show that when jamming attacks are restricted so that the wireless channel is not subject to long consecutive emissions of high powered interference signals, then the first moment of the state stays bounded. Interestingly, even under such restrictions, the wireless channel may be attacked at all time instants with small interference powers and thus for any finite interval, there is always a positive probability that all transmission attempts may fail. In this aspect, our setting differs from the deterministic case, where the maximum possible length of a continuous attack duration is required to be bounded to ensure input-to-state stability under disturbance.

As a first step, we investigate the scenarios where the norm of the disturbance is bounded almost surely at each time by a fixed scalar. In such scenarios, the first moment of the state is bounded under attacks from an attacker with sufficiently small resources. Then we explore the more general case where the distribution of the disturbance norm may have infinite support. For this case, we obtain an inequality for the 