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

Xuekang Zhang (), Huisheng Shu () and Haoran Yi ()
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Xuekang Zhang: Anhui Polytechnic University
Huisheng Shu: Donghua University
Haoran Yi: Donghua University

Journal of Theoretical Probability, 2023, vol. 36, issue 1, 78-98

Abstract: 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.

Keywords: Ornstein–Uhlenbeck processes; Small Lévy noises; Least squares estimator; Consistency; Asymptotic distribution; 60G52; 62F12 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01170-4

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