Berry-Ess 'een bound for drift estimation of fractional Ornstein\n Uhlenbeck process of second kind

2020/05/17 by Maoudo Faramba Baldé, Balde, Maoudo Faramba, Rachid Belfadli +3
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · #Advanced Queuing Theory Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2005.08397

openalex publication_date 2020/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we consider the Ornstein-Uhlenbeck process of the second\nkind defined as solution to the equation dX_t = -\α\nX_tdt+dY_t⁽¹⁾,\n X₀=0, where Y_t⁽¹⁾:=\∫₀^te^-sdB^H_a_s with\na_t=He^\(t)/(H), and B^H is a fractional Brownian motion with Hurst\nparameter H\∈( frac12,1), whereas \α>0 is unknown parameter to be\nestimated. We obtain the upper bound O(1/\√(T)) in Kolmogorov distance for\nnormal approximation of the least squares estimator of the drift parameter\n\α on the basis of the continuous observation X_t,t\∈[0,T] , as\nT\→\∞. Our method is based on the work of citekp-JVA, which\nis proved using a combination of Malliavin calculus and Stein's method for\nnormal approximation.\n

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