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Parameter Estimation for Ornstein–Uhlenbeck Driven by Ornstein–Uhlenbeck Processes with Small Lévy Noises

Author

Listed:
  • Xuekang Zhang

    (Anhui Polytechnic University
    Donghua University)

  • Huisheng Shu

    (Donghua University)

  • Haoran Yi

    (Donghua University)

Abstract

In this paper, we consider the problem of parameter estimation for Ornstein–Uhlenbeck driven by Ornstein–Uhlenbeck processes with small Lévy noises, based on discrete observations at n regularly spaced time points $$t_i=i/n,i=1,2,\ldots ,n,$$ t i = i / n , i = 1 , 2 , … , n , on [0, 1]. Under certain conditions, we obtain the consistency and the rate of convergence of the least squares estimator when a small dispersion parameter $$\epsilon $$ ϵ tends to 0 and $$n\rightarrow \infty $$ n → ∞ simultaneously. Additionally, the asymptotic distribution of the estimator is established.

Suggested Citation

  • Xuekang Zhang & Huisheng Shu & Haoran Yi, 2023. "Parameter Estimation for Ornstein–Uhlenbeck Driven by Ornstein–Uhlenbeck Processes with Small Lévy Noises," Journal of Theoretical Probability, Springer, vol. 36(1), pages 78-98, March.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:1:d:10.1007_s10959-022-01170-4
    DOI: 10.1007/s10959-022-01170-4
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    References listed on IDEAS

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