  Renewal theorems are developed for point processes with interarrival times
$W_n=\xi(X_{n+1}X_n\cdots)$, where $(X_n)_{n\in\mathbb Z}$ is a stochastic
process with finite state space $\Sigma$ and $\xi\colon\Sigma_A\to\mathbb R$ is
a H\"older continuous function on a subset $\Sigma_A\subset\Sigma^{\mathbb N}$.
The theorems developed here unify and generalise the key renewal theorem for
discrete measures and Lalley's renewal theorem for counting measures in
symbolic dynamics. Moreover, they capture aspects of Markov renewal theory. The
new renewal theorems allow for direct applications to problems in fractal and
hyperbolic geometry; for instance, results on the Minkowski measurability of
self-conformal sets are deduced. Indeed, these geometric problems motivated the
development of the renewal theorems.
