Stochastic analysis of cyber-attacks

Abstract

After studying the stochastic process of cyber-attacks against a cyber system, we investigate the set of intermediate times between successive cyber-attacks. Then, we give basic definitions and properties on the expected number of cyber-attacks in a closed time interval and present renewal theorems, as well as a description of exact and asymptotic probability distributions for the main occurrence moments of cyber-attacks. Further, we outline stationary renewal processes of cyber-attacks. The paper concludes with asymptotic properties for the counting function of cyber-attacks.