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arXiv · 2401.00053

Some extremal problems for martingale transforms, I

Vasily Vasyunin·Pavel Zatitskii
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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.

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Vasily Vasyunin, Pavel Zatitskii. 2023-12-29. Some extremal problems for martingale transforms, I. https://arxiv.org/abs/2401.00053

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