  Bitcoin is a electronic payment system where payment transactions are
verified and stored in a data structure called the blockchain. Bitcoin miners
work individually to solve a computationally intensive problem, and with each
solution a Bitcoin block is generated, resulting in a new arrival to the
blockchain. The difficulty of the computational problem is updated every 2,016
blocks in order to control the rate at which blocks are generated. In the
original Bitcoin paper, it was suggested that the blockchain arrivals occur
according to a homogeneous Poisson process. Based on blockchain block arrival
data and stochastic analysis of the block arrival process, we demonstrate that
this is not the case. We present a refined mathematical model for block
arrivals, focusing on both the block arrivals during a period of constant
difficulty and how the difficulty level evolves over time.
