Donsker's theorem in {Wasserstein}-1 distance

By using Theorem 2 and by applying some outer affine transformations we can easily replace the field inverses with arbitrary affine-equivalent functions and therefore with

The absolute magnitude M and apparent magnitude m of a Cepheid star can be also related by the distance modulus equation (1), and its distance d can be

In this paper, we study in the Markovian case the rate of convergence in the Wasserstein distance of an approximation of the solution to a BSDE given by a BSDE which is driven by

— When M is a smooth projective algebraic variety (type (n,0)) we recover the classical Lefschetz theorem on hyperplane sections along the lines of the Morse theoretic proof given

As a corollary we show in section 4 that if 3f is a projective manifold with ample canonical bundle then there is a bound, depending only on the Chern numbers of

This not only allows us to relate topological dynamical systems to linear dynamical systems but also provide a new class of hypercyclic operators acting on Lipschitz-free spaces..

In other words, no optimal rates of convergence in Wasserstein distance are available under moment assumptions, and they seem out of reach if based on current available

Thanks to our result of invertibility of the Jacobian matrix of the flow, we can also prove (Theorem 2 in §4 ) that the process thus defined is a solution to a linear