  A discrete-time random process is described which can generate bursty
sequences of events. A Bernoulli process, where the probability of an event
occurring at time $t$ is given by a fixed probability $x$, is modified to
include a memory effect where the event probability is increased proportionally
to the number of events which occurred within a given amount of time preceding
$t$. For small values of $x$ the inter-event time distribution follows a
power-law with exponent $-2-x$. We consider a dynamic network where each node
forms, and breaks connections according to this process. The value of $x$ for
each node depends on the fitness distribution, $\rho(x)$, from which it is
drawn; we find exact solutions for the expectation of the degree distribution
for a variety of possible fitness distributions, and for both cases where the
memory effect either is, or is not present. This work can potentially lead to
methods to uncover hidden fitness distributions from fast changing, temporal
network data such as online social communications and fMRI scans.
