Nonparametric estimation of the trend for stochastic differential equations driven by small α-stable noises

Publication date: Available online 22 March 2019Source: Statistics & Probability LettersAuthor(s): Xuekang Zhang, Haoran Yi, Huisheng ShuAbstractThe present paper deals with the problem of nonparametric estimation of the trend for stochastic differential equations driven by small α-stable noises based on continuous-time observation. Under some certain conditions, we derive the uniform consistency and the rate of convergence of the nonparametric estimator. Besides, the asymptotic distribution of the estimator in our setting is shown to be a stable distribution.

Source: Statistics and Probability Letters - March 24, 2019 Category: Statistics Source Type: research