On maximal inequalities for purely discontinuous $L_q$-valued martingales

Carlo Marinelli

On maximal inequalities for purely discontinuous $L_q$-valued martingales

Probability 2013-11-28 v1

Authors: Carlo Marinelli

Abstract

We prove maximal inequalities for $L_q$ -valued martingales obtained by stochastic integration with respect to compensated random measures. A version of these estimates for integrals with respect to compensated Poisson random measures were first obtained by Dirksen (arXiv:1208:3885) using arguments based on inequalities for sums of independent Banach-space-valued random variables, geometric properties of Banach spaces, and decoupling inequalities. Our proofs are completely different and rely almost exclusively on classical stochastic analysis for real semimartingales.

Keywords

maximal inequalities discontinuous martingales $L_q$-valued martingales stochastic integration compensated random measures semimartingales

Cite

@article{arxiv.1311.7120,
  title  = {On maximal inequalities for purely discontinuous $L_q$-valued martingales},
  author = {Carlo Marinelli},
  journal= {arXiv preprint arXiv:1311.7120},
  year   = {2013}
}

Comments

14 pages

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