Weak convergence to the fractional Brownian sheet in Besov spaces

被引：11

作者：

Tudor, CA ^{[1
]}

机构：

[1] Univ Paris 06, Lab Probabil & Modeles Aleatoires, F-75252 Paris 5, France

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2003年 / 34卷 / 03期

关键词：

fractional brownian motion; weak convergence; Besov spaces;

D O I：

10.1007/s00574-003-0020-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the problem of the approximation in law of the fractional Brownian sheet in the topology of the anisotropic Besov spaces. We prove the convergence in law of two families of processes to the fractional Brownian sheet: the first family is constructed from a Poisson procces in the plane and the second family is defined by the partial sums of two sequences of real independent fractional brownian motions.

引用

页码：389 / 400

页数：12

共 50 条

[31] Fractional wavelets, derivatives, and Besov spaces
Unser, M
Blu, T
WAVELETS: APPLICATIONS IN SIGNAL AND IMAGE PROCESSING X, PTS 1 AND 2, 2003, 5207 : 147 - 152
[32] ON THE RATE OF CONVERGENCE IN NON-CENTRAL ASYMPTOTICS OF THE HERMITE VARIATIONS OF FRACTIONAL BROWNIAN SHEET
Breton, Jean-Christophe
PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 2011, 31 (02): : 301 - 311
[33] Weak convergence of integral functionals of random walks weakly convergent to fractional Brownian motion
Mishura Yu.S.
Rode S.H.
Ukrainian Mathematical Journal, 2007, 59 (8) : 1155 - 1162
[34] Degree of convergence of Fourier series in Besov spaces
Nigam, H. K.
JOURNAL OF ANALYSIS, 2023, 31 (03): : 2265 - 2285
[35] Degree of convergence of Fourier series in Besov spaces
H. K. Nigam
The Journal of Analysis, 2023, 31 : 2265 - 2285
[36] Stochastic differential equations driven by a Wiener process and fractional Brownian motion: Convergence in Besov space with respect to a parameter
Mishura, Yu. S.
Posashkova, S. V.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) : 1166 - 1180
[37] WEAK CONVERGENCE OF REFLECTING BROWNIAN MOTIONS
Burdzy, Krzysztof
Chen, Zhen-Qing
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 1998, 3 : 29 - 33
[38] HERMITE VARIATIONS OF THE FRACTIONAL BROWNIAN SHEET
Reveillac, Anthony
Stauch, Michael
Tudor, Ciprian A.
STOCHASTICS AND DYNAMICS, 2012, 12 (03)
[39] WEAK-CONVERGENCE TO BROWNIAN EXCURSION
BLUMENTHAL, RM
ANNALS OF PROBABILITY, 1983, 11 (03): : 798 - 800
[40] Jumps in Besov spaces and fine properties of Besov and fractional Sobolev functions
Paz Hashash
Arkady Poliakovsky
Calculus of Variations and Partial Differential Equations, 2024, 63

← 1 2 3 4 5 →