The law of iterated logarithm for the estimations of diffusion-type processes

[摘要] This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexity argument, it is proved that the estimator for different values of γ satisfies the iterated logarithm law. The result also presents the exponential convergence principle for the estimator converging to the true value.

[学科分类] 航空航天科学

[关键词] The law of iterated logarithm;Diffusion-type processes;Approach of argmins;Objective function