$\boldsymbol{\alpha}$ -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

Abstract

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

CLC Number:

O211

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

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