$ L_{\infty} $-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise

Huiping Jiao; Xiao Zhang; Chao Wei; Huiping Jiao; Xiao Zhang; Chao Wei

doi:10.3934/math.2023107

AIMS Mathematics

2023, Volume 8, Issue 1: 2083-2092. doi: 10.3934/math.2023107

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Research article

$ L_{\infty} $-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise

1.
School of Basic Science, Zhengzhou University of Technology, Zhengzhou 450044, China
2.
School of Marxism, Anyang Normal University, Anyang 455000, China
3.
School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China

Received: 16 August 2022 Revised: 13 October 2022 Accepted: 19 October 2022 Published: 27 October 2022
MSC : 60H10, 62F12

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 $.
Citation: Huiping Jiao, Xiao Zhang, Chao Wei. $ L_{\infty} $-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise[J]. AIMS Mathematics, 2023, 8(1): 2083-2092. doi: 10.3934/math.2023107

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Abstract

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 $.

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