Copulas encompass the entire dependence structure of multivariate distributions, and not only the correlations. Together with the marginal distributions of the vector elements, they define a multivariate distribution which can be used to generate random vectors with this distribution. A toolbox is presented which implements input models with this method, for random vectors and time series. Time...

The aim of this paper is to derive some consequences of the main result of Götze and Zaitsev [5] (see Theorem 2 below). We shall show that the i.i.d. case of this result implies the multidimensional version of a result of Sakhanenko [12]. We shall obtain bounds for the rate of strong Gaussian approximation of sums of i.i.d. R-valued random vectors ξj having finite moments E ‖ξj‖ , γ > 2. We con...

We de ne a covariance-type operator on Wiener space: for F and G two random variables in the Gross-Sobolev space D of random variables with a square-integrable Malliavin derivative, we let ΓF,G:= ⟨ DF,−DL−1G ⟩ , where D is the Malliavin derivative operator and L−1 is the pseudo-inverse of the generator of the Ornstein-Uhlenbeck semigroup. We use Γ to extend the notion of covariance and canonica...

We define a covariance-type operator on Wiener space: for F and G two random variables in the Gross-Sobolev space D of random variables with a square-integrable Malliavin derivative, we let ΓF,G:= 〈 DF,−DL−1G 〉 where D is the Malliavin derivative operator and L−1 is the pseudo-inverse of the generator of the Ornstein-Uhlenbeck semigroup. We use Γ to extend the notion of covariance and canonical...