Volatility Estimation of Gaussian Ornstein–Uhlenbeck Processes of the Second Kind

Rachid Belfadli (), Khalifa Es-Sebaiy () and Fatima-Ezzahra Farah ()
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Rachid Belfadli: Cadi Ayyad University
Khalifa Es-Sebaiy: Kuwait University
Fatima-Ezzahra Farah: Cadi Ayyad University

Journal of Theoretical Probability, 2023, vol. 36, issue 1, 1-17

Abstract: Abstract In this paper, under suitable assumptions on the Gaussian process $$G=\lbrace G_t,\,t\ge 0\rbrace $$ G = { G t , t ≥ 0 } , we establish results on uniform convergence in probability and in law stably for the realized power variation of the Riemann–Stieljes integral $$Z_t=\int _0^t u_s \text {d}Y_{s,G}^{(1)}$$ Z t = ∫ 0 t u s d Y s , G ( 1 ) with respect to $${Y_{t,G}^{(1)}}=\int _0^t \text {e}^{-s} \text {d}G_{a(s)}$$ Y t , G ( 1 ) = ∫ 0 t e - s d G a ( s ) , where u is a process of finite q-variation with $$q

Keywords: Gaussian process; Realized power variation; Stable convergence; Integrated volatility; Riemann–Stieljes integral; 60G15; 60G22; 62F12; 91G80 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-023-01238-9

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