Local scaling limits of Lévy driven fractional random fields

in Bernoulli (in press)

Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces

in Bernoulli (2020), 26(3), 2202-2225

In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the scope of Riemannian ... [more ▼]

In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the scope of Riemannian geometry. Firstly, we consider sub-Riemannian limits of Riemannian foliations. Secondly, we consider the non-smooth setting of RCD*(K,N) spaces. In each case the necessary ingredients are an Ito formula and a comparison theorem for the Laplacian, for which we refer to the recent literature. As an application, we derive pointwise Carmona-type estimates on eigenfunctions of Schrodinger operators. [less ▲]

Estimation of the linear fractional stable motion

in Bernoulli (2020), 26(1), 226252

Universal Gaussian fluctuations on the discrete Poisson chaos

in Bernoulli (2014), 20(2), 697-715

Maximum likelihood characterization of distributions

in Bernoulli (2014), 20(2), 775-802

A famous characterization theorem due to C. F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and ... [more ▼]

A famous characterization theorem due to C. F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There exist many extensions of this result in diverse directions, most of them focussing on location and scale families. In this paper we propose a unified treatment of this literature by providing general MLE characterization theorems for one-parameter group families (with particular attention on location and scale parameters). In doing so we provide tools for determining whether or not a given such family is MLE-characterizable, and, in case it is, we define the fundamental concept of minimal necessary sample size at which a given characterization holds. Many of the cornerstone references on this topic are retrieved and discussed in the light of our findings, and several new characterization theorems are provided. Of particular interest is that one part of our work, namely the introduction of so-called equivalence classes for MLE characterizations, is a modernized version of Daniel Bernoulli's viewpoint on maximum likelihood estimation. [less ▲]

A Bernstein-type inequality for suprema of random processes with applications to model selection in non-Gaussian regression

in Bernoulli (2010), 16(4), 1064--1085

Limit theorems for nonlinear functionals of Volterra processes via white noise analysis

in Bernoulli (2010), 16(4), 1262-1293

Central limit theorems for double Poisson integrals

in Bernoulli (2008), 14(3), 791--821

Correcting Newton-Cotes integrals by Lévy areas

in Bernoulli (2007), 13(3), 695-711

Explicit formulae for time-space Brownian chaos

in Bernoulli (2003), 9(1), 25--48