Model-adaptive optimal discretization of stochastic integrals*

We study the optimal discretization error of stochastic integrals driven by a multidimensional continuous Brownian semimartingale. In the previous works a pathwise lower bound for the renormalized quadratic variation of the error was provided together with an asymptotically optimal discretization strategy, i.e. for which the lower bound is attained. However the construction of the optimal strategy involved the knowledge about the diffusion coefficient of the semimartingaleunder study. In this work we provide a model-adaptive asymptotically optimal discretization strategy that does not require any prior knowledge about the model. We prove the optimality for quite general class of discretization strategies based on kernel techniques for adaptive estimation and previously obtained optimal strategies that use random ellipsoid hitting times.