Some extremal problems for martingale transforms, I
Classical Analysis and ODEs
2024-01-02 v1 Analysis of PDEs
Probability
Abstract
With this paper, we begin a series of studies of extremal problems for estimating distributions of martingale transforms of bounded martingales. The Bellman functions corresponding to such problems are pointwise minimal diagonally concave functions on a horizontal strip, satisfying certain given boundary conditions. We describe the basic structures that arise when constructing such functions and present a solution in the case of asymmetric boundary conditions and a sufficiently small width of the strip.
Cite
@article{arxiv.2401.00053,
title = {Some extremal problems for martingale transforms, I},
author = {Vasily Vasyunin and Pavel Zatitskii},
journal= {arXiv preprint arXiv:2401.00053},
year = {2024}
}