Asymptotic statistical equivalence for ergodic diffusions
- Dalalyan, Arnak
- Reiß, Markus
2010 Mathematics Subject Classification
- 62B15 62C05 62G20 62M99
- Asymptotic equivalence, statistical experiment, Le Cam distance, ergodic diffusion, mixed Gaussian white noise
For scalar diffusion models with unknown drift function asymptotic equivalence in the sense of Le Cam's deficiency between statistical experiments is considered for long-time asymptotics. A local asymptotic equivalence result is established with an accompanying sequence of simple Gaussian shift experiments. Corresponding globally asymptotically equivalent experiments are obtained as compound experiments. The results are extended in several directions including time discretisation.
- Probab. Theory Related Fields