Monografie Matematyczne

Sharp Martingale and Semimartingale Inequalities

Authors: Osękowski, Adam

  • Aims at a detailed explanation of Burkholder's method: presents, for most estimates, the steps leading to the discovery of the corresponding special functions
  • Uses diverse analytic and probabilistic methods to solve the corresponding boundary value problems
  • Presents a unified up-to-date treatment, illustrated on a variety of examples of different type, difficulty and complexity
  • Material is completely self-contained
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About this book

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.​  

Table of contents (8 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0370-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0348-0369-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-0348-0749-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Sharp Martingale and Semimartingale Inequalities
Authors
Series Title
Monografie Matematyczne
Series Volume
72
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0370-0
DOI
10.1007/978-3-0348-0370-0
Hardcover ISBN
978-3-0348-0369-4
Softcover ISBN
978-3-0348-0749-4
Series ISSN
0077-0507
Edition Number
1
Number of Pages
XII, 464
Topics