A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions

• Autorzy: Adam Osękowski
• Języki publikacji: EN

Abstrakty

EN

Let X be a submartingale starting from 0, and Y be a semimartingale which is orthogonal and strongly differentially subordinate to X. The paper contains the proof of the sharp estimate
$ℙ(sup_{t≥0} |Y_t| ≥ 1) ≤ 3.375... ∥X∥₁$.
As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.

Kategorie tematyczne

• 31B05: Harmonic, subharmonic, superharmonic functions
• 60G44: Martingales with continuous parameter

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: 59
• Numer: 3
• Strony: 261-274

Daty

wydano

2011

Twórcy

autor

Adam Osękowski

• Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba59-3-7