In a traditional High Performance Computing system, it is possible to process a huge data volume. The nature of events in classic High Performance computing is static. In Distributed Exa-scale System has a different nature. The processing Big data in a distributed exascale system evokes a new challenge. The dynamic and interactive character of a distributed exascale system changes processes status and system elements. This paper discusses the challenge that Big data attributes: volume, velocity, variety, how they influence distributed exascale system dynamic and interactive nature. While investigating the effect of the Dynamic and Interactive nature of exascale systems in computing Big data, this research work suggests the Markov chains model. This model suggests the transition matrix, which identifies system status and memory sharing. It lets us analyze the two systems convergence. As a result in both systems are explored by the influence of each other.