Applications of pathwise Burkholder-Davis-Gundy inequalities

2015/07/05 by Siorpaes, Pietro
#60G44 #FOS: Mathematics #Primary 60G42 #Probability (math.PR) #Secondary 91G20

paper · doi:10.48550/arxiv.1507.01302

Abstract

We present several applications of the pathwise Burkholder-Davis-Gundy (BDG) inequalities. Most importantly we prove them for cadlag semimartingales and a general function Φ, and use this to derive BDG inequalities (non-pathwise ones) for the Bessel process of order α≥ 1 and for martingales stopped at τ, with τ in a well studied class of random times.

Related

• Burkholder inequalities for submartingales, Bessel processes and conformal martingales
• The Burkholder-Davis-Gundy Inequality for Enhanced Martingales
• Burkholder's submartingales from a stochastic calculus perspective
• On the maximal inequalities of Burkholder, Davis and Gundy
• The Sharp Constant for the Burkholder-Davis-Gundy Inequality and Non-Smooth Pasting