Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (1): 249-260.

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

Xuekang Zhang1,*(),Shanlin Wan1(),Huisheng Shu2()   

  1. 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)


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