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Research Article | Open Access

L ∞ -norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise

Huiping Jiao1, Xiao Zhang2, Chao Wei3( )
School of Basic Science, Zhengzhou University of Technology, Zhengzhou 450044, China
School of Marxism, Anyang Normal University, Anyang 455000, China
School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China
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Abstract

This paper is concerned with L ∞ -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 ε → 0.

Keywords

L∞-norm minimum distance estimationstochastic differential equationssmall fractional Lévy noiseconsistency, asymptotic distribution
CLC number: 60H10, 62F12

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AIMS Mathematics
Volume 8 Issue 1,
January 2023
Pages 2083-2092
DOI: 10.3934/math.2023107

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Cite this article:
Jiao H, Zhang X, Wei C. L ∞ -norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise. AIMS Mathematics, 2023, 8(1): 2083-2092. https://doi.org/10.3934/math.2023107

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Received: 16 August 2022
Revised: 13 October 2022
Accepted: 19 October 2022
Published: 15 January 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)