  We prove Berry-Esseen type rates of convergence for central limit theorems
(CLTs) of regenerative processes which generalize previous results of
Bolthausen under weaker moment assumptions. We then show how this general
result can be applied to obtain rates of convergence for (1) CLTs for additive
functionals of positive recurrent Markov chains under certain conditions on the
strong mixing coefficients, and (2) annealed CLTs for certain ballistic random
walks in random environments.
