Sharp Martingale and Semimartingale Inequalities

• Main Author: Osękowski, Adam (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2012.
• Series: Monografie Matematyczne ; 72
• Subjects: Mathematics.; Functional analysis.; Potential theory (Mathematics).; Probabilities.; Probability Theory and Stochastic Processes.; Potential Theory.; Functional Analysis.

This monograph presents 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 1980s,...

Table of Contents:

• Preface.- 1. Introduction.- 2. Burkholder’s method.- 3. Martingale inequalities in discrete time.- 4. Sub- and supermartingale inequalities in discrete time.- 5. Inequalities in continuous time.- 6. Inequalities for orthogonal semimartingales.- 7. Maximal inequalities.- 8. Square function inequalities
• Appendix
• Bibliography.