Some extremal problems for martingale transforms, I
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917557280178176 |
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| 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 |