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portada sharp martingale and semimartingale inequalities
Type
Physical Book
Author
Publisher
Year
2012
Language
English
Pages
464
Format
Hardcover
Dimensions
23.4x15.5x3 cm
Weight
0.79 kg.
ISBN
3034803699
ISBN13
9783034803694
Categories

sharp martingale and semimartingale inequalities

Adam Osękowski (Author) · Birkhauser · Hardcover

sharp martingale and semimartingale inequalities - Osękowski, Adam

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Synopsis "sharp martingale and semimartingale inequalities"

This monograph is a presentation of a unified approach to a certain class of semimartingale inequalities, which can be regarded as probabilistic extensions of classical estimates for conjugate harmonic functions on the unit disc. The approach, which has its roots in the seminal works of Burkholder in the 80s, enables to deduce a given inequality for semimartingales from the existence of a certain special function with some convex-type properties. Remarkably, an appropriate application of the method leads to the sharp version of the estimate under investigation, which is particularly important for applications. These include the theory of quasiregular mappings (with deep implications to the geometric function theory); the boundedness of two-dimensional Hilbert transform and a more general class of Fourier multipliers; the theory of rank-one convex and quasiconvex functions; and more. The book is divided into a few separate parts. In the introductory chapter we present motivation for the results and relate them to some classical problems in harmonic analysis. The next part contains a general description of the method, which is applied in subsequent chapters to the study of sharp estimates for discrete-time martingales; discrete-time sub- and supermartingales; continuous time processes; the square and maximal functions. Each chapter contains additional bibliographical notes included for reference.​

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