Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bou...Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.展开更多
In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate devi...In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate deviations,as well as the moderation deviation principle with explicit rate function can be obtained.展开更多
基金supported by Deutsche Forschungsgemeinschaft (DFG) (Grant No. ME 4473/2-1)the Centre Henri Lebesgue (CHL) (Grant No. ANR-11-LABX-0020-01)National Natural Science Foundation of China (Grants Nos. 11971063, 11731012, 12271062 and 12288201)。
文摘Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.
基金supported by the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20231435)Fundamental Research Funds for the Central Universities(Grant No.NS2022069)supported by Natural Science Foundation of Zhejiang Province(Grant No.LY19A010004)。
文摘In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate deviations,as well as the moderation deviation principle with explicit rate function can be obtained.