Download Sharp Martingale and Semimartingale Inequalities: 72 by Adam Osękowski PDF

By Adam Osękowski

This monograph is a presentation of a unified method of a undeniable classification of semimartingale inequalities, that are considered as probabilistic extensions of classical estimates for conjugate harmonic services at the unit disc. The strategy, which has its roots within the seminal works of Burkholder within the 80s, allows to infer a given inequality for semimartingales from the life of a definite designated functionality with a few convex-type homes. Remarkably, a suitable software of the tactic ends up in the pointy model of the estimate less than research, that is fairly vital for functions. those comprise the speculation of quasiregular mappings (with deep implications to the geometric functionality theory); the boundedness of two-dimensional Hilbert rework and a extra basic type of Fourier multipliers; the idea of rank-one convex and quasiconvex features; and more.
The publication is split right into a few separate elements. within the introductory bankruptcy we current motivation for the implications and relate them to a few classical difficulties in harmonic research. the subsequent half incorporates a basic description of the tactic, that is utilized in next chapters to the examine of sharp estimates for discrete-time martingales; discrete-time sub- and supermartingales; non-stop time strategies; the sq. and maximal features. every one bankruptcy includes extra bibliographical notes integrated for reference.​

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