Some extremal problems for martingale transforms, I

Fuente: arXiv
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Main Authors: Vasyunin, Vasily, Zatitskii, Pavel
Format: Preprint
Published: 2023
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_version_ 1866917557280178176
author Vasyunin, Vasily
Zatitskii, Pavel
author_facet Vasyunin, Vasily
Zatitskii, Pavel
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2401_00053
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Some extremal problems for martingale transforms, I
Vasyunin, Vasily
Zatitskii, Pavel
Classical Analysis and ODEs
Analysis of PDEs
Probability
42B35, 60G42, 60G46
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.
title Some extremal problems for martingale transforms, I
topic Classical Analysis and ODEs
Analysis of PDEs
Probability
42B35, 60G42, 60G46
url https://arxiv.org/abs/2401.00053