The Davis Inequality

Part of the Indian Statistical Institute Series book series (INSIS)


In this chapter, we would give the continuous-time version of the Burkholder–Davis–Gundy inequality \(-p=1\) case. This is due to Davis. This plays an important role in answering various questions on the stochastic integral w.r.t. a martingale M—including condition on \(f\in {\mathbb L}(M)\) under which \(\int f\,d\, M\) is a local martingale. This naturally leads us to the notion of a sigma-martingale which we discuss. We will begin with a result on martingales obtained from process with a single jump.

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Chennai Mathematical InstituteSiruseriIndia

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