Regularization lemmas and convergence in total variation

Autor: Lucia Caramellino, Guillaume Poly, Vlad Bally

Publikováno v: Electronic Journal of Probability
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2020, 25, paper no. 74, 20 pp. ⟨10.1214/20-EJP481⟩
Electron. J. Probab.
Electronic Journal of Probability, 2020, 25, paper no. 74, 20 pp. ⟨10.1214/20-EJP481⟩

We provide a simple abstract formalism of integration by parts under which we obtain some regularization lemmas. These lemmas apply to any sequence of random variables $(F_n)$ which are smooth and non-degenerated in some sense and enable one to upgra

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d5d5f2efc46ae8835307224ae60b5d27
https://hal.archives-ouvertes.fr/hal-02429512/file/RegLemmaVar-18-09-2019.pdf

Total variation distance between stochastic polynomials and invariance principles

Autor: Vlad Bally, Lucia Caramellino

Publikováno v: Annals of Probability
Annals of Probability, Institute of Mathematical Statistics, 2019, 47, pp.3762-3811. ⟨10.1214/19-AOP1346⟩
Ann. Probab. 47, no. 6 (2019), 3762-3811
Annals of Probability, 2019, 47, pp.3762-3811. ⟨10.1214/19-AOP1346⟩

International audience; The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence, one obtains an in-variance principle for such polynomials. This generalizes known results concern

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a987a9f5a257e95e0014b74dd21eed0
https://hal-upec-upem.archives-ouvertes.fr/hal-02429560

Asymptotic development for the CLT in total variation distance

Autor: Lucia Caramellino, Vlad Bally

Publikováno v: Bernoulli
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2016, 22, pp.2442-2485
Bernoulli 22, no. 4 (2016), 2442-2485
Bernoulli, 2016, 22, pp.2442-2485

International audience; The aim of this paper is to study the asymptotic expansion in total variation in the Central Limit Theorem when the law of the basic random variable is locally lower-bounded by the Lebesgue measure (or equivalently, has an abs

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a26c469a11f7f1c8bb2a61c73a05567e
https://hal.archives-ouvertes.fr/hal-01104866

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