$\boldsymbol{\alpha}$ -稳定过程驱动的非线性随机微分方程的参数估计: 非遍历情形

数学物理学报 ›› 2023, Vol. 43 ›› Issue (1): 249-260.

$\boldsymbol{\alpha}$ -稳定过程驱动的非线性随机微分方程的参数估计: 非遍历情形

张雪康^1,^*(),万山林¹(),舒慧生²()

¹安徽工程大学数理与金融学院安徽芜湖241000
²东华大学理学院上海201620

收稿日期:2021-04-22 修回日期:2022-07-05 出版日期:2023-02-26 发布日期:2023-03-07
通讯作者: ^*张雪康, E-mail: xkzhang@ahpu.edu.cn
作者简介:万山林, E-mail: 2221020107@stu.ahpu.edu.cn|舒慧生, E-mail: hsshu@dhu.edu.cn
基金资助:
国家自然科学基金(12101004);国家自然科学基金(62073071);国家自然科学基金(12271003);安徽工程大学引进人才科研启动基金(2020YQQ064);安徽省高端装备智能控制国际联合研究中心开放基金(IRICHE-05)

Parameter Estimation for Nonlinear Stochastic Differential Equations Driven by $\boldsymbol\alpha$-Stable Processes: Non-ergodic Case

Zhang Xuekang^1,^*(),Wan Shanlin¹(),Shu Huisheng²()

¹School of Mathematics-Physics and Finance, Anhui Polytechnic University, Anhui Wuhu 241000
²College of Science, Donghua University, Shanghai 201620

Received:2021-04-22 Revised:2022-07-05 Online:2023-02-26 Published:2023-03-07
Supported by:
The NSFC(12101004);The NSFC(62073071);The NSFC(12271003);Startup Foundation for Introducing Talent of Anhui Polytechnic University(2020YQQ064);Open Project of Anhui Province Center for International Reasearch of Intelligent Control of High-end Equipment(IRICHE-05)

摘要/Abstract

摘要：

该文研究了基于连续时间状态观测的 $\alpha$ -稳定过程驱动非线性随机微分方程的参数估计问题. 首先, 讨论了加权拟合估计量的相合性和收敛速率. 随后, 建立了估计量的渐近分布.

关键词: 非遍历情形, $\alpha$-稳定过程, 非线性随机微分方程, 相合性, 渐近分布

Abstract:

The present paper deals with the parameter estimation problem for nonlinear stochastic differential equations driven by $\alpha$-stable processes based on continuous-time observation. We first discuss the consistency and the rate of convergence of the weighted trajectory fitting estimator. Then, we have established the asymptotic distribution of the estimator.

Key words: Non-ergodic case, $\alpha$-stable processes, Nonlinear stochastic differential equations, Consistency, Asymptotic distribution

中图分类号:

O211

张雪康, 万山林, 舒慧生. $\boldsymbol{\alpha}$ -稳定过程驱动的非线性随机微分方程的参数估计: 非遍历情形[J]. 数学物理学报, 2023, 43(1): 249-260.

Zhang Xuekang, Wan Shanlin, Shu Huisheng. Parameter Estimation for Nonlinear Stochastic Differential Equations Driven by $\boldsymbol\alpha$-Stable Processes: Non-ergodic Case[J]. Acta mathematica scientia,Series A, 2023, 43(1): 249-260.

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