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. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
Original languageEnglish
Pages (from-to)735-766
Number of pages32
JournalJournal of Mathematical Sciences
Volume284
Issue number6
DOIs
StatePublished - 26 Sep 2024

ID: 126355210