Distribution of martingales with bounded square functions |
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| Institution: | 1. St. Petersburg State University, Department of Mathematics and Computer Science, 14th line 29B, Vailuevsky Island, St. Petersburg, Russia;2. St. Petersburg Department of Steklov Mathematical Institute RAS, Fontanka 27, St. Petersburg, Russia;3. Department of Mathematics and Physics, University of Stavanger, Stavanger, Norway |
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| Abstract: | We study the terminate distribution of a martingale whose square function is bounded. We obtain sharp estimates for the exponential and p-moments, as well as for the distribution function itself. The proofs are based on the elaboration of the Burkholder method and on the investigation of certain locally concave functions. |
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