L<sub>∞</sub>-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise
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 t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023107?viewType=HTML |
| _version_ | 1798023151382167552 |
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| author | Huiping Jiao Xiao Zhang Chao Wei |
| author_facet | Huiping Jiao Xiao Zhang Chao Wei |
| author_sort | Huiping Jiao |
| collection | DOAJ |
| description | 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 $. |
| first_indexed | 2024-04-11T17:41:42Z |
| format | Article |
| id | doaj.art-ee664bc265ef42029f7efba781bb6d48 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T17:41:42Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ee664bc265ef42029f7efba781bb6d482022-12-22T04:11:29ZengAIMS PressAIMS Mathematics2473-69882023-01-01812083209210.3934/math.2023107L<sub>∞</sub>-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noiseHuiping Jiao0Xiao Zhang1Chao Wei 21. School of Basic Science, Zhengzhou University of Technology, Zhengzhou 450044, China2. School of Marxism, Anyang Normal University, Anyang 455000, China3. School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, ChinaThis 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 $.https://www.aimspress.com/article/doi/10.3934/math.2023107?viewType=HTMLl<sub>∞</sub>-norm minimum distance estimationstochastic differential equationssmall fractional lévy noiseconsistencyasymptotic distribution |
| spellingShingle | Huiping Jiao Xiao Zhang Chao Wei L<sub>∞</sub>-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise AIMS Mathematics l<sub>∞</sub>-norm minimum distance estimation stochastic differential equations small fractional lévy noise consistency asymptotic distribution |
| title | L<sub>∞</sub>-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise |
| title_full | L<sub>∞</sub>-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise |
| title_fullStr | L<sub>∞</sub>-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise |
| title_full_unstemmed | L<sub>∞</sub>-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise |
| title_short | L<sub>∞</sub>-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise |
| title_sort | l sub ∞ sub norm minimum distance estimation for stochastic differential equations driven by small fractional levy noise |
| topic | l<sub>∞</sub>-norm minimum distance estimation stochastic differential equations small fractional lévy noise consistency asymptotic distribution |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023107?viewType=HTML |
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