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January 2003 Maximal inequalities for a series of continuous local martingales
Litan Yan, Ying Guo
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SUT J. Math. 39(1): 71-83 (January 2003). DOI: 10.55937/sut/1059541396


Let {Xj=(Xtj,t),j1} be a sequence of continuous local martingales and {Xj} the corresponding sequence of their quadratic variation processes and let Hn(x,y),n=1,2, be the Hermite polynomials with parametric variable y.

In this paper, we consider the series j=1Hn2(Xj,Xj) of the continuous local martingales


and its discrete analogue, and obtain some maximal inequalities.


The first author would like to thank Professor N. Kazamaki for his guidance and kindness on the study of martingales and related fields. The authors wish also to thank an anonymous earnest referee for a careful reading of the manuscript and some helpful comments.


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Litan Yan. Ying Guo. "Maximal inequalities for a series of continuous local martingales." SUT J. Math. 39 (1) 71 - 83, January 2003.


Received: 3 February 2003; Published: January 2003
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1059541396

Primary: 60G42 , 60G44 , 60H05

Keywords: continuous local martingale , Hermite polynomials , series of martingales and martingale transform , the Barlow-Yor inequalities , the Burkholder-Davis-Gundy inequalities

Rights: Copyright © 2003 Tokyo University of Science

Vol.39 • No. 1 • January 2003
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