Prohorov-Type Local Limit Theorems on Abstract Wiener Spaces

Paley-wiener-type Theorems

The Fourier transforms of functions with compact and convex supports in R are described. The Fourier transforms of functions with nonconvex and unbounded supports are also considered.

Almost sure central limit theorems on the Wiener space

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian elds. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution.

Quantitative stable limit theorems on the Wiener space

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize previous works by Nourdin and Nualart [J. Theoret. Probab. 23 (2010) 39–64] and Harnett and Nualart [Stochastic Process. Appl. 122 (2012) 3460–3505], and pr...

On Local and Ratio Limit Theorems

Abstract Korovkin-type theorems in modular spaces and applications

Korovkin-type theorems in modular spaces and applications C. Bardaro ∗ A. Boccuto † X. Dimitriou ‡ I. Mantellini § Abstract We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results even with respect to an axiomatic convergence, whose...