Almost sure absolute continuity of Bernoulli convolutions
Björklund, Michael ; Schnellmann, Daniel
Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010), p. 888-893 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

La continuité absolue, presque sûrement, est démontrée dans une classe de convolutions de Bernoulli symétrique, étendant un résultat de Peres et Solomyak.

We prove an extension of a result by Peres and Solomyak on almost sure absolute continuity in a class of symmetric Bernoulli convolutions.

Publié le : 2010-01-01
DOI : https://doi.org/10.1214/09-AIHP334
Classification:  60Exx,  60G50 
@article{AIHPB_2010__46_3_888_0,
     author = {Bj\"orklund, Michael and Schnellmann, Daniel},
     title = {Almost sure absolute continuity of Bernoulli convolutions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {46},
     year = {2010},
     pages = {888-893},
     doi = {10.1214/09-AIHP334},
     mrnumber = {2682271},
     zbl = {1204.28004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2010__46_3_888_0}
}

Björklund, Michael; Schnellmann, Daniel. Almost sure absolute continuity of Bernoulli convolutions. Annales de l'I.H.P. Probabilités et statistiques, Tome 46 (2010) pp. 888-893. doi : 10.1214/09-AIHP334. http://gdmltest.u-ga.fr/item/AIHPB_2010__46_3_888_0/

[1] B. Jessen and A. Wintner. Distribution functions and the Riemann Zeta function. Trans. Amer. Math. Soc. 38 (1935) 48-88. | JFM 61.0462.03 | MR 1501802

[2] R. Kershner and A. Wintner. On symmetric Bernoulli convolutions. Amer. J. Math. 57 (1935) 541-548. | JFM 61.0464.02 | MR 1507093

[3] Y. Peres and B. Solomyak. Absolute continuity of Bernoulli convolutions, a simple proof. Math. Res. Lett. 3 (1996) 231-239. | MR 1386842 | Zbl 0867.28001

[4] B. Solomyak. On the random series ∑±λn (an Erdös problem). Ann. of Math. (2) 142 (1995) 611-625. | MR 1356783 | Zbl 0837.28007

[5] A. Wintner. On analytic convolutions of Bernoulli distributions. Amer. J. Math. 56 (1934) 659-663. | MR 1507049 | Zbl 0010.05905

[6] A. Wintner. On symmetric Bernoulli convolutions. Bull. Amer. Math. Soc. 41 (1935) 137-138. | JFM 61.0464.01 | MR 1563036

[7] A. Wintner. On convergent Poisson convolutions. Amer. J. Math. 57 (1935) 827-838. | JFM 61.0465.02 | MR 1507116