We investigate nonparametric drift estimation for multidimensional jump diffusions based on continuous observations. The results are derived under anisotropic smoothness assumptions and the estimators' performance is measured in terms of the sup-norm loss. We present two different Nadaraya--Watson type estimators, which are both shown to achieve the classical nonparametric rate of convergence under varying assumptions on the jump measure. Fully data-driven versions of both estimators are also introduced and shown to attain the same rate of convergence. The results rely on novel uniform moment bounds for empirical processes associated to the investigated jump diffusion, which are of independent interest.

翻译：摘要：本文基于连续观测数据研究多维跳跃扩散过程的非参数漂移估计。在异质光滑性假设下推导结论，并通过超范数损失度量估计量的性能。我们提出了两种不同的Nadaraya-Watson型估计量，两者均被证明在跳跃测度的不同假设条件下能够达到经典非参数收敛速率。同时引入了两种估计量的完全数据驱动版本，并证明其能实现相同的收敛速率。研究结果依赖于与所考察跳跃扩散过程相关的经验过程的新型均匀矩估计，该结果具有独立研究价值。