Weak convergence of error processes in discretizations of stochastic integrals and Besov spaces

被引：24

作者：

Geiss, Stefan ^{[1
]}

Toivola, Anni ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, FIN-40014 Jyvaskyla, Finland

来源：

BERNOULLI | 2009年 / 15卷 / 04期

关键词：

approximation; Besov spaces; stochastic integrals; weak convergence; SOBOLEV SPACES; WEIGHTED BMO; APPROXIMATION; DISTRIBUTIONS;

D O I：

10.3150/09-BEJ197

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider weak convergence of the rescaled error processes arising from Riemann discretizations of certain stochastic integrals and relate the L(p)-integrability of the weak limit to the fractional smoothness in the Malliavin sense of the stochastic integral

引用

页码：925 / 954

页数：30

共 50 条

[1] Weak convergence of summation processes in Besov spaces
Morel, B
STUDIA MATHEMATICA, 2004, 165 (01) : 19 - 37
[2] WEAK CONVERGENCE OF STOCHASTIC INTEGRALS RELATED TO COUNTING PROCESSES
AALEN, OO
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1977, 38 (04): : 261 - 277
[3] Weak convergence towards a class of Gaussian processes in anisotropic Besov spaces
Boufoussi, Brahim
Guerbaz, Raby
BULLETIN DES SCIENCES MATHEMATIQUES, 2006, 130 (07): : 612 - 623
[4] Weak convergence of stochastic integrals
Szyszkowski, I
THEORY OF PROBABILITY AND ITS APPLICATIONS, 1997, 41 (04) : 810 - 814
[5] REPRESENTATION AND WEAK CONVERGENCE OF STOCHASTIC INTEGRALS WITH FRACTIONAL INTEGRATOR PROCESSES
Davidson, James
Hashimzade, Nigar
ECONOMETRIC THEORY, 2009, 25 (06) : 1589 - 1624
[6] Weak convergence to the fractional Brownian sheet in Besov spaces
Tudor, CA
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2003, 34 (03): : 389 - 400
[7] Weak convergence to the fractional Brownian sheet in Besov spaces
Ciprian A. Tudor
Bulletin of the Brazilian Mathematical Society, 2003, 34 : 389 - 400
[8] Weak convergence in Besov spaces to fractional Brownian motion
Boufoussi, B
Lakhel, EH
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (01): : 39 - 44
[9] Weak convergence of stochastic integrals and differential equations
Kurtz, Thomas G.
Protter, Philip E.
Lecture Notes in Mathematics, 1627
[10] Weak convergence to a class of multiple stochastic integrals
Sun, Xichao
Yan, Litan
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (17) : 8355 - 8368

← 1 2 3 4 5 →