In this paper, we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting. We first describe a more general model of blockchain selfish mining with both a two-block leading competitive criterion and a new economic incentive mechanism. Then we establish a pyramid Markov process and show that it is irreducible and positive recurrent, and its stationary probability vector is matrix-geometric with an explicitly representable rate matrix. Also, we use the stationary probability vector to study the influence of many orphan blocks on the waste of computing resource. Next, we set up a pyramid Markov reward process to investigate the long-run average profits of the honest and dishonest mining pools, respectively. As a by-product, we build three approximative Markov processes and provide some new interesting interpretation on the Markov chain and the revenue analysis reported in the seminal work by Eyal and Sirer (2014). Note that the pyramid Markov (reward) processes can open up a new avenue in the study of blockchain selfish mining. Thus we hope that the methodology and results developed in this paper shed light on the blockchain selfish mining such that a series of promising research can be developed potentially.

翻译：在本文中,我们提供了金字塔马可夫流程的新理论框架,以解决在严格数学环境下的封闭式自私采矿业某些开放和根本性的开放和基本问题。我们首先描述一个更普遍的软链自私采矿模式,其模式有两块领先的竞争标准和新的经济激励机制。然后,我们建立了一个金字塔马可夫流程,显示它不可减损和正重复,其固定概率矢量是矩阵-几何,并有一个明确代表率矩阵。此外,我们利用固定概率矢量来研究许多孤儿块对计算资源浪费的影响。接下来,我们设置了一个金字塔马可夫奖项进程,分别调查诚实和不诚实采矿池的长期平均利润。作为副产品,我们建立了三个相似的马可夫流程,对马尔可夫链流程和Eyal和Sirer (2014)报告的收入分析提供了一些新的有趣解释。注意金字塔马可(反向)流程可以在块自私采矿研究中开辟一条新途径。因此我们希望本文中制定的方法和结果能够使这一块自私链采矿研究成为具有前景的系列。