We consider a multidimensional diffusion process whose drift and diffusion coefficients depend respectively on a parameter and . This process is observed at equally spaced times , and denotes the length of the `observation window'. We are interested in estimating and/or . Under suitable smoothness and identifiability conditions, we exhibit estimators and , such that the variables and are tight for and . When is known, we can even drop the assumption that . These results hold without any kind of ergodicity or even recurrence assumption on the diffusion process.
"Parametric inference for discretely observed non-ergodic diffusions." Bernoulli 12 (3) 383 - 401, June 2006. https://doi.org/10.3150/bj/1151525127