SUT J. Math. 39 (1), 71-83, (January 2003) DOI: 10.55937/sut/1059541396
KEYWORDS: Hermite polynomials, the Burkholder-Davis-Gundy inequalities, the Barlow-Yor inequalities, continuous local martingale, series of martingales and martingale transform, 60G44, 60G42, 60H05
Let be a sequence of continuous local martingales and the corresponding sequence of their quadratic variation processes and let be the Hermite polynomials with parametric variable .
In this paper, we consider the series of the continuous local martingales
and its discrete analogue, and obtain some maximal inequalities.