Multidimensional Stein's method for Gamma ...
Document type :
Pré-publication ou Document de travail
Title :
Multidimensional Stein's method for Gamma approximation
Author(s) :
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Zurcher, Jérémy [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Zurcher, Jérémy [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Publication date :
2023-05-06
English keyword(s) :
60F05 60G15 60H05 60H07 Stein's method Stein's equation Gamma approximation Malliavin calculus multiple stochastic integrals asymptotic independence
60F05
60G15
60H05
60H07 Stein's method
Stein's equation
Gamma approximation
Malliavin calculus
multiple stochastic integrals
asymptotic independence
60F05
60G15
60H05
60H07 Stein's method
Stein's equation
Gamma approximation
Malliavin calculus
multiple stochastic integrals
asymptotic independence
HAL domain(s) :
Mathématiques [math]/Probabilités [math.PR]
English abstract : [en]
Let F (ν) be the centered Gamma law with parameter ν > 0 and let us denote by P Y the probability distribution of a random vector Y. We develop a multidimensional variant of the Stein's method for Gamma approximation that ...
Show more >Let F (ν) be the centered Gamma law with parameter ν > 0 and let us denote by P Y the probability distribution of a random vector Y. We develop a multidimensional variant of the Stein's method for Gamma approximation that allows to obtain bounds for the second Wasserstein distance between the probability distribution of an arbitrary random vector (X, Y) in R × R n and the probability distribution F (ν) ⊗ P Y. In the case of random vectors with components in Wiener chaos, these bounds lead to some interesting criteria for the joint convergence of a sequence ((X n , Y n), n ≥ 1) to F (ν) ⊗ P Y , by assuming that (X n , n ≥ 1) converges in law, as n → ∞, to F (ν) and (Y n , n ≥ 1) converges in law, as n → ∞, to an arbitrary random vector Y. We illustrate our criteria by two concrete examples.Show less >
Show more >Let F (ν) be the centered Gamma law with parameter ν > 0 and let us denote by P Y the probability distribution of a random vector Y. We develop a multidimensional variant of the Stein's method for Gamma approximation that allows to obtain bounds for the second Wasserstein distance between the probability distribution of an arbitrary random vector (X, Y) in R × R n and the probability distribution F (ν) ⊗ P Y. In the case of random vectors with components in Wiener chaos, these bounds lead to some interesting criteria for the joint convergence of a sequence ((X n , Y n), n ≥ 1) to F (ν) ⊗ P Y , by assuming that (X n , n ≥ 1) converges in law, as n → ∞, to F (ν) and (Y n , n ≥ 1) converges in law, as n → ∞, to an arbitrary random vector Y. We illustrate our criteria by two concrete examples.Show less >
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Anglais
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