A uniform key renewal theorem is deduced from the uniform Blackwell's renewal theorem. A uniform LDP (large deviation principle) for renewal-reward processes is obtained, and MDP (moderate deviation principle) is deduced under conditions much weaker than existence of exponential moments.
"From uniform renewal theorem to uniform large and moderate deviations for renewal-reward processes." Electron. Commun. Probab. 18 1 - 13, 2013. https://doi.org/10.1214/ECP.v18-2719