24 citations · 66 across the 9 of their papers we have counts for
14 papers
On the Malliavin calculus on product spaces and an infinite de Jong theorem
Christian Döbler
We extend the Malliavin theory for -functionals on product probability spaces that has recently been developed independently by Decreusefond and Halconruy (2019) and by Duerin…
The Berry-Esseen bound in de Jong's CLT
Christian Döbler
We prove a Berry-Esseen bound in de Jong's classical CLT for normalized, completely degenerate -statistics, which says that the convergence of the fourth moment sequence to thre…
A short proof of Lévy's continuity theorem without using tightness
Christian Döbler
In this note we present a new short and direct proof of Lévy's continuity theorem in arbitrary dimension , which does not rely on Prohorov's theorem, Helly's selection theorem o…
The multivariate functional de Jong CLT
Christian Döbler, Mikołaj Kasprzak, Giovanni Peccati
We prove a multivariate functional version of de Jong's CLT (1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics, the corresponding empirical proc…
Functional Convergence of Sequential U-processes with Size-Dependent Kernels
Christian Döbler, Mikołaj Kasprzak, Giovanni Peccati
We consider sequences of -processes based on symmetric kernels of a fixed order, that possibly depend on the sample size. Our main contribution is the derivation of a set of ana…
Fourth moment theorems on the Poisson space in any dimension
Christian Döbler, Anna Vidotto, Guangqu Zheng
We extend to any dimension the quantitative fourth moment theorem on the Poisson setting, recently proved by C. Döbler and G. Peccati (2017). In particular, by adapting the exchang…
The fourth moment theorem on the Poisson space
Christian Döbler, Giovanni Peccati
We prove an exact fourth moment bound for the normal approximation of random variables belonging to the Wiener chaos of a general Poisson random measure. Such a result -- that has…
The Gamma Stein equation and non-central de Jong theorems
Christian Döbler, Giovanni Peccati
We study the Stein equation associated with the one-dimensional Gamma distribution, and provide novel bounds, allowing one to effectively deal with test functions supported by the…
Quantitative de Jong theorems in any dimension
Christian Döbler, Giovanni Peccati
We develop a new quantitative approach to a multidimensional version of the well-known {\it de Jong's central limit theorem} under optimal conditions, stating that a sequence of Ho…
An iterative technique for bounding derivatives of solutions of Stein equations
Christian Döbler, Robert E. Gaunt, Sebastian J. Vollmer
We introduce a simple iterative technique for bounding derivatives of solutions of Stein equations , where is a linear differential operator and is the…
Recurrence for the frog model with drift on
Christian Döbler, Lorenz Pfeifroth
In this paper we present a recurrence criterion for the frog model on with an i.i.d. initial configuration of sleeping frogs and such that the underlying random walk…
Distributional transformations without orthogonality relations
Christian Döbler
Distributional transformations characterized by equations relating expectations of test functions weighted by a given biasing function on the original distribution to expectations…
A quantitative central limit theorem for linear statistics of random matrix eigenvalues
Christian Döbler, Michael Stolz
It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the co…
Stein's method and the multivariate CLT for traces of powers on the classical compact groups
Christian Döbler, Michael Stolz
Let be a random element of the unitary, special orthogonal, or unitary symplectic groups, distributed according to Haar measure. By a classical result of Diaconis and Shahsha…