On uniform laws of large numbers for ergodic diffusions and consistency of estimators (Q1412242)

For a regular diffusion with normalized speed measure \(\mu\) a law of large numbers uniform with respect to a class \({F}\) is proved if \({F}\) has a \(\mu\)-integrable envelope function or if \({F}\) is bounded in \({L_p}\) for some \(p>1\). The result is used to improve consistency results for the local time estimator and for a class of simple M-estimators.