Central limit theorem for Hölder processes on m -unit cube

Jana Klicnarová

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 1, page 83-91
  • ISSN: 0010-2628

Abstract

top
We consider a sequence of stochastic processes ( X n ( 𝐭 ) , 𝐭 [ 0 , 1 ] m ) with continuous trajectories and we show conditions for the tightness of the sequence in the Hölder space with a parameter γ .

How to cite

top

Klicnarová, Jana. "Central limit theorem for Hölder processes on $\mathbb {R}^m$-unit cube." Commentationes Mathematicae Universitatis Carolinae 48.1 (2007): 83-91. <http://eudml.org/doc/250188>.

@article{Klicnarová2007,
abstract = {We consider a sequence of stochastic processes $(X_n(\mathbf \{t\}), \mathbf \{t\}\in [0,1]^m)$ with continuous trajectories and we show conditions for the tightness of the sequence in the Hölder space with a parameter $\gamma $.},
author = {Klicnarová, Jana},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Hölder space; tightness; weak convergence; Hölder space; tightness; weak convergence},
language = {eng},
number = {1},
pages = {83-91},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Central limit theorem for Hölder processes on $\mathbb \{R\}^m$-unit cube},
url = {http://eudml.org/doc/250188},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Klicnarová, Jana
TI - Central limit theorem for Hölder processes on $\mathbb {R}^m$-unit cube
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 1
SP - 83
EP - 91
AB - We consider a sequence of stochastic processes $(X_n(\mathbf {t}), \mathbf {t}\in [0,1]^m)$ with continuous trajectories and we show conditions for the tightness of the sequence in the Hölder space with a parameter $\gamma $.
LA - eng
KW - Hölder space; tightness; weak convergence; Hölder space; tightness; weak convergence
UR - http://eudml.org/doc/250188
ER -

References

top
  1. Billingsley P., Convergence of Probability Measures, Wiley, New York. Zbl0944.60003MR1700749
  2. Ledoux M., Talagrand M., Probability in Banach Spaces, Springer, New York. Zbl0748.60004
  3. Lamperti J., On convergence of stochastic processes, Trans. Amer. Math. Soc. 104 430-435. Zbl0113.33502MR0143245
  4. Hamadouche D., Invariance principles in Hölder spaces, Portugal. Math. 57 127-153. Zbl0965.60011MR1759810
  5. Kerkyacharian G., Roynette B., Une démonstration simple des théorèmes de Kolmogorov, Donsker et Ito-Nisio, C.R. Acad. Sci. Paris Sér. Math. I 312 877-882. Zbl0764.60008MR1108512
  6. Račkauskas A., Suquet C., Random fields and central limit theorem in some generalized Hölder spaces, Proceedings of the 7th international Vilnius conference, pp.599-616. 
  7. Račkauskas A., Suquet C., Invariance principles for adaptive self-normalized partial sums processes, Stochastic Process. Appl. 95 63-81. MR1847092
  8. Račkauskas A., Suquet C., Central limit theorems in Hölder topologies for Banach space valued random fields, Theory Probab. Appl. 49 1 77-92. MR2141332

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.