L ∞ " role="presentation" style="position: relative;"> L ∞ L ∞ L_{\infty} -norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise

AIMS Mathematics

article

Huiping Jiao¹  Xiao Zhang²  Chao Wei³ 

[1] School of Basic Science, Zhengzhou University of Technology;School of Marxism, Anyang Normal University;School of Mathematics and Statistics, Anyang Normal University

关键词: $ L_{\infty} $-norm minimum distance estimation;    stochastic differential equations;    small fractional Lévy noise;    consistency;    asymptotic distribution;   

DOI  :  10.3934/math.2023107

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

This paper is concerned with $ L_{\infty} $-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise. By applying the Gronwall-Bellman lemma, Chebyshev's inequality and Taylor's formula, the minimum distance estimator is established and the consistency and asymptotic distribution of the estimator are derived when a small dispersion coefficient $ \varepsilon\rightarrow 0 $.

【 授权许可】

CC BY