Limiting behavior of relative R\'enyi entropy in a non-regular location   shift family
  We calculate the limiting behavior of relative Renyi entropy when the first probability distribution is close to the second one in a non-regular location-shift family which is generated by a probability distribution whose support is an interval or a half-line. This limit can be regarded as a generalization of Fisher information, and plays an important role in large deviation theory. 
Masahito Hayashi