Geodesic
On distances between distributions of polynomials
Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 79-85 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We estimate total variation distances between distributions of polynomials via $L^2$-norms.
Keywords: Gaussian measure, logarithmically concave measure.
Mots-clés : Distribution of a polynomial, total variation norm 
@article{THSP_2017_22_2_a7,
     author = {Georgii I. Zelenov},
     title = {On distances between distributions of polynomials},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {79--85},
     year = {2017},
     volume = {22},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a7/}
}
TY  - JOUR
AU  - Georgii I. Zelenov
TI  - On distances between distributions of polynomials
JO  - Teoriâ slučajnyh processov
PY  - 2017
SP  - 79
EP  - 85
VL  - 22
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a7/
LA  - en
ID  - THSP_2017_22_2_a7
ER  - 
%0 Journal Article
%A Georgii I. Zelenov
%T On distances between distributions of polynomials
%J Teoriâ slučajnyh processov
%D 2017
%P 79-85
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a7/
%G en
%F THSP_2017_22_2_a7
Georgii I. Zelenov. On distances between distributions of polynomials. Teoriâ slučajnyh processov, Tome 22 (2017) no. 2, pp. 79-85. http://geodesic.mathdoc.fr/item/THSP_2017_22_2_a7/

[1] Sbornik Math., 206:8 (2015), 1030–1048 | DOI | DOI | MR | Zbl

[2] Russian Math. Surveys, 71:4 (216), 703–749 | DOI | DOI | MR | Zbl

[3] V. I. Bogachev, E. D. Kosov, G. I. Zelenov, “Fractional smoothness of distributions of polynomials and a fractional analog of the Hardy–Landau–Littlewood inequality”, Trans. Amer. Math. Soc., 370:6 (2018), 4401–4432 | DOI | MR | Zbl

[4] Dokl. Math., 91:2 (2015), 138–141 | DOI | MR | Zbl

[5] Dokl. Math., 94:2 (2016), 453–457 | DOI | MR | Zbl

[6] V. I. Bogachev, Gaussian measures, Amer. Math. Soc., Providence, Rhode Island, 1998 | MR | Zbl

[7] V. I. Bogachev, Differentiable measures and the Malliavin calculus, Amer. Math. Soc., Providence, Rhode Island, 2010 | MR | Zbl

[8] A. Carbery, J. Wright, “Distributional and $L_q$ norm inequalities for polynomials over convex bodies in ${\mathbb R}^n$”, Math. Research Lett., 8:3 (2001), 233–248 | DOI | MR | Zbl

[9] Y. A. Davydov, “On distance in total variation between image measures”, Statistics Probability Letters, 129 (2017), 393–400 | DOI | MR | Zbl

[10] Y. A. Davydov, G. V. Martynova, “Limit behavior of multiple stochastic integral”, Statistics and Control of Random Processes, Nauka, Preila, Moscow, 1987, 55–57 (Russian) | MR

[11] E. D. Kosov, “Fractional smoothness of images of logarithmically concave measures under polynomials”, J. Math. Anal. Appl., 462:1 (2018), 390–406 | DOI | MR | Zbl

[12] G. V. Martynova, Limit theorems for the functionals of random procceses, Candidate of science dissertation (PhD thesis), Russian State Library (Moscow), N 1-1-5/LGU, Leningrad, 1987 (Russian)

[13] I. Nourdin, G. Poly, “Convergence in total variation on Wiener chaos”, Stochastic Process. Appl., 123:2 (2013), 651–674 | DOI | MR | Zbl

[14] D. Nualart, The Malliavin calculus and related topics, 2nd ed., Springer-Verlag, Berlin, 2006 | MR | Zbl