This talk focuses on our recent research on Markov Processes in Blockchain Systems. The blockchain systems are established as multi-dimensional Markov processes by means of the longest chain rule of chain-fork structure. We address several interesting issues or topics related to the multi-dimensional Markov processes. This further sets up mathematical models and develops economic theory of blockchain. Here, we shall care for:

(1) How to study the multi-dimensional Markov processes, for example, stable conditions, steady-state probability, first passage time, sojourn time and so forth. Perhaps the Markov processes bring you to enter a queer theoretical space from such an interesting practical technology.

(2) Block reward, transaction fee and their allocation methods greatly motivate many miners in a blockchain to take shape some selfish mining alliances evolutionarily, while the selfish mining alliances will lead to various attacks on security of blockchain. As a first exploration, we provide a unified and comprehensive framework for expressing the attacks grown out of the selfish mining alliances, a physical structure of which is given a detailed observation and interpretation in terms of the Markov processes. This may be viewed as a key improvement in the study of blockchain mining management. On the other hand, our method can also be developed to analyze blochchain systems through some simple and intuitive applications of Markov decision processes and stochastic game modeling.

(3) We show that the multi-dimensional Markov processes will play an important role in the study of blockchain systems and in the design of consensus mechanism of related distributed systems. Also, they can motivate a series of promising future research on development of blockchain technologies.