On Necessary and Sufficient Conditions in the Functional Central Limit Theorem for Semimartingales

R. Sh. Liptser; A. N. Shiryaev

doi:10.1137/1126010

On Necessary and Sufficient Conditions in the Functional Central Limit Theorem for Semimartingales

Theory of Probability and Its Applications ◽

10.1137/1126010 ◽

1981 ◽

Vol 26 (1) ◽

pp. 130-135 ◽

Cited By ~ 10

Author(s):

R. Sh. Liptser ◽

A. N. Shiryaev

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Functional Central Limit Theorem ◽

Necessary And Sufficient ◽

Functional Central Limit

Download Full-text

On a problem of necessary and sufficient conditions in the functional central limit theorem for local martingales

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete ◽

10.1007/bf00532223 ◽

1982 ◽

Vol 59 (3) ◽

pp. 311-318 ◽

Cited By ~ 16

Author(s):

R. Sh. Liptser ◽

A. N. Shiryaev

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Functional Central Limit Theorem ◽

Necessary And Sufficient ◽

Functional Central Limit

Download Full-text

Necessary and sufficient conditions on rates of convergence in the multidimensional central limit theorem

manuscripta mathematica ◽

10.1007/bf01954614 ◽

1979 ◽

Vol 28 (4) ◽

pp. 361-377 ◽

Cited By ~ 1

Author(s):

R. Michel

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Sufficient Conditions ◽

Rates Of Convergence ◽

Necessary And Sufficient Conditions ◽

Multidimensional Central Limit Theorem ◽

Necessary And Sufficient

Download Full-text

Necessary and Sufficient Condition for the Functional Central Limit Theorem in Hölder Spaces

Journal of Theoretical Probability ◽

10.1023/b:jotp.0000020482.66224.6c ◽

2004 ◽

Vol 17 (1) ◽

pp. 221-243 ◽

Cited By ~ 21

Author(s):

Alfredas Račkauskas ◽

Charles Suquet

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Functional Central Limit Theorem ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Hölder Spaces ◽

Necessary And Sufficient ◽

Holder Spaces ◽

Functional Central Limit

Download Full-text

Necessary and sufficient conditions for the moving blocks bootstrap central limit theorem of the mean

Journal of Nonparametric Statistics ◽

10.1080/10485251003663517 ◽

2012 ◽

Vol 24 (2) ◽

pp. 343-357 ◽

Cited By ~ 4

Author(s):

Dragan Radulović

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Moving Blocks Bootstrap ◽

The Mean ◽

Necessary And Sufficient ◽

Bootstrap Central Limit Theorem

Download Full-text

Necessary and sufficient conditions for the conditional central limit theorem

10.1214/aop/1029867121 ◽

2002 ◽

Vol 30 (3) ◽

pp. 1044-1081 ◽

Cited By ~ 34

Author(s):

Jérôme Dedecker ◽

Florence Merlevède

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Conditional Central Limit Theorem ◽

Necessary And Sufficient

Download Full-text

On necessary and sufficient conditions for the self-normalized central limit theorem

Science China Mathematics ◽

10.1007/s11425-018-9368-3 ◽

2018 ◽

Vol 61 (10) ◽

pp. 1741-1748 ◽

Cited By ~ 3

Author(s):

Qiman Shao

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

The Self ◽

Necessary And Sufficient

Download Full-text

Functional Central Limit Theorem approximations and the distribution of the Dickey–Fuller test with strongly heteroskedastic data

Economics Letters ◽

10.1016/j.econlet.2004.09.008 ◽

2005 ◽

Vol 86 (3) ◽

pp. 427-433 ◽

Cited By ~ 5

Author(s):

Rossen Valkanov

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Functional Central Limit Theorem ◽

Functional Central Limit

Download Full-text

A Hölderian functional central limit theorem for a multi-indexed summation process

Stochastic Processes and their Applications ◽

10.1016/j.spa.2006.12.006 ◽

2007 ◽

Vol 117 (8) ◽

pp. 1137-1164 ◽

Cited By ~ 2

Author(s):

Alfredas Račkauskas ◽

Charles Suquet ◽

Vaidotas Zemlys

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Functional Central Limit Theorem ◽

Summation Process ◽

Functional Central Limit

Download Full-text

A Functional Central Limit Theorem for Positively Dependent Random Variables

Journal of Multivariate Analysis ◽

10.1006/jmva.1993.1018 ◽

1993 ◽

Vol 44 (2) ◽

pp. 314-320 ◽

Cited By ~ 19

Author(s):

T. Birkel

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Random Variables ◽

Functional Central Limit Theorem ◽

Dependent Random Variables ◽

Functional Central Limit

Download Full-text

A Functional Central Limit Theorem for Semimartingales

Theory of Probability and Its Applications ◽

10.1137/1125084 ◽

1981 ◽

Vol 25 (4) ◽

pp. 667-688 ◽

Cited By ~ 54

Author(s):

R. Sh. Liptser ◽

A. N. Shiryayev

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Functional Central Limit Theorem ◽

Functional Central Limit

Download Full-text