Adaptive sequential estimation for ergodic diffusion processes in   quadratic metric. Part 2: Asymptotic efficiency
  Asymptotic efficiency is proved for the constructed in part 1 procedure, i.e. Pinsker's constant is found in the asymptotic lower bound for the minimax quadratic risk. It is shown that the asymptotic minimax quadratic risk of the constructed procedure coincides with this constant. 
Leonid Galtchouk (IRMA), Serguey Pergamenshchikov (LMRS)