Nous établissons une formule asymptotique exacte pour la variation quadratique de certains processus de sommes partielles. Soit
We establish an exact asymptotic formula for the square variation of certain partial sum processes. Let
@article{AIHPB_2015__51_4_1597_0, author = {Lewko, Allison and Lewko, Mark}, title = {An exact asymptotic for the square variation of partial sum processes}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {1597--1619}, publisher = {Gauthier-Villars}, volume = {51}, number = {4}, year = {2015}, doi = {10.1214/14-AIHP617}, mrnumber = {3414459}, zbl = {1329.60066}, language = {en}, url = {https://www.numdam.org/articles/10.1214/14-AIHP617/} }
TY - JOUR AU - Lewko, Allison AU - Lewko, Mark TI - An exact asymptotic for the square variation of partial sum processes JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2015 SP - 1597 EP - 1619 VL - 51 IS - 4 PB - Gauthier-Villars UR - https://www.numdam.org/articles/10.1214/14-AIHP617/ DO - 10.1214/14-AIHP617 LA - en ID - AIHPB_2015__51_4_1597_0 ER -
%0 Journal Article %A Lewko, Allison %A Lewko, Mark %T An exact asymptotic for the square variation of partial sum processes %J Annales de l'I.H.P. Probabilités et statistiques %D 2015 %P 1597-1619 %V 51 %N 4 %I Gauthier-Villars %U https://www.numdam.org/articles/10.1214/14-AIHP617/ %R 10.1214/14-AIHP617 %G en %F AIHPB_2015__51_4_1597_0
Lewko, Allison; Lewko, Mark. An exact asymptotic for the square variation of partial sum processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 4, pp. 1597-1619. doi : 10.1214/14-AIHP617. https://www.numdam.org/articles/10.1214/14-AIHP617/
[1]
[2] Probability Theory: Independence, Interchangeability, Martingales, 3rd edition. Springer, Berlin, 1997. | MR | Zbl
and .[3] Stochastic Processes. Wiley, New York, 1953. | MR | Zbl
.
[4] Empirical processes and
[5] On some classical results in probability theory. Sankhyā Ser. A 47 (1985) 215–221. | MR | Zbl
.[6] Advanced Probability Theory, 2nd edition. Dekker, New York, 1995. | MR | Zbl
.[7] On the law of the iterated logarithm. Amer. J. Math. 63 (1941) 169–176. | DOI | JFM | MR
and .[8] Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 (301) (1963) 13–30. | MR | Zbl
.[9] Variation inequalities for the Fejér and Poisson kernels. Trans. Amer. Math. Soc. 356 (11) (2004) 4493–4518. | MR | Zbl
and .[10] Estimates for the square variation of partial sums of Fourier series and their rearrangements. J. Funct. Anal. 262 (6) (2012) 2561–2607. | MR | Zbl
and .[11] Orthonormal systems in linear spans. Anal. PDE 7 (2014) 97–115. | DOI | MR | Zbl
and .[12] A variational Barban–Davenport–Halberstam theorem. J. Number Theory 132 (9) (2012) 2020–2045. | MR | Zbl
and .[13] The square variation of rearranged Fourier series. Amer. J. Math. To appear, 2015. Available at arXiv:1212.1988. | DOI | MR | Zbl
and .
[14] The
[15] Théorie asymptotique des processus aléatoires faiblement dépendants. Mathématiques and Applications 31. Springer, Berlin, 1999. | MR | Zbl
.
[16] On the subspaces of
[17] Exact asymptotic estimates of Brownian path variation. Duke Math. J. 39 (1972) 219–241. | DOI | MR | Zbl
.Cité par Sources :