Parametric inference for discretely observed non-ergodic diffusions

Abstract

SUMMARY: We consider a multidimensional diusion process X whose drift and diusion coecien ts de- pend respectively on a parameter and . This process is observed at n + 1 equally{spaced times 0; n; 2 n;:::;n n, and Tn = n n denotes the length of the \observation window". We are interested in estimating and/or . Under suitable smoothness and identiabilit y conditions, we exhibit estimators b n and b n, such that the variables p n (b n ) and p Tn (b n ) are tight, as soon as n! 0 and Tn!1. When is known, we can even drop the assumption Tn!1. The novelty is that these results hold without any kind of ergodicity or even recurrence assumption on the diusion process.