  This paper presents a stochastic model for block arrival times based on the
difficulty retargeting rule used in Bitcoin, as well as other proof-of-work
blockchains. Unlike some previous work, this paper explicitly models the
difficulty target as a random variable which is a function of the previous
block arrival times and affecting the block times in the next retargeting
period. An explicit marginal distribution is derived for the time between
successive blocks (the blocktime), while allowing for randomly changing
difficulty. This paper also aims to serve as an introduction to Bitcoin and
proof-of-work blockchains for the controls community, focusing on the
difficulty retargeting procedure used in Bitcoin.
