Advertisement

Martingales

  • Tuomas HytönenEmail author
  • Jan van Neerven
  • Mark Veraar
  • Lutz Weis
Chapter
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics book series (MATHE3, volume 63)

Abstract

This chapter is a lengthy introduction to the general theory of discrete-time martingales, biased towards the needs of the subsequent chapters. Throughout, we discuss martingales with a σ-finite measure space domain and a Banach space range, but the development is self-contained and does not assume any results from the conventional set-up of a probability space domain and/or a real-valued range. Each section is devoted to a different aspect of the martingale theory, including norm inequalities, convergence results, decompositions and transforms, and norm approximation of general martingales by simpler ones. This systematic development of the general martingale theory will substantially streamline the discussion of UMD spaces in the subsequent chapter.

Keywords

Banach Space Maximal Function Maximal Inequality Dyadic Cube Nirenberg Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Tuomas Hytönen
    • 1
    Email author
  • Jan van Neerven
    • 2
  • Mark Veraar
    • 3
  • Lutz Weis
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  3. 3.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  4. 4.Department of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany

Personalised recommendations