Sharp Maximal Inequality for Martingales and Stochas- Tic Integrals

  • ADAM OSȨKOWSKI
  • Published 2008

Abstract

Let X = (X t)t≥0 be a martingale and H = (Ht)t≥0 be a predictable process taking values in [−1,1]. Let Y denote the stochastic integral of H with respect to X . We show that || sup t≥0 Yt ||1 ≤ β0|| sup t≥0 |X t |||1, where β0 = 2,0856 . . . is the best possible. Furthermore, if, in addition, X is nonnegative, then || sup t≥0 Yt ||1 ≤ β 0 || sup t≥0 X t ||1… (More)

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Cite this paper

@inproceedings{OSKOWSKI2008SharpMI, title={Sharp Maximal Inequality for Martingales and Stochas- Tic Integrals}, author={ADAM OSȨKOWSKI}, year={2008} }