In this paper we study the properties of the Lasso estimator of the drift component in the diffusion setting. More specifically, we consider a multivariate parametric diffusion model $X$ observed continuously over the interval $[0,T]$ and investigate drift estimation under sparsity constraints. We allow the dimensions of the model and the parameter space to be large. We obtain an oracle inequality for the Lasso estimator and derive an error bound for the $L^2$-distance using concentration inequalities for linear functionals of diffusion processes. The probabilistic part is based upon elements of empirical processes theory and, in particular, on the chaining method.

翻译：本文研究了扩散过程中漂移分量的Lasso估计量性质。具体而言，我们考虑在区间[0,T]上连续观测的多元参数化扩散模型$X$，并在稀疏性约束下研究漂移估计问题。允许模型维度和参数空间维度较大。我们获得了Lasso估计量的oracle不等式，并利用扩散过程线性泛函的集中不等式推导了$L^2$距离的误差界。概率论部分基于经验过程理论，特别是链式方法。