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Algebraic polynomials and moments of stochastic integrals
We propose an algebraic method for proving estimates on moments of stochastic
integrals. The method uses qualitative properties of roots of algebraic
polynomials from certain general classes. As an application, we give a new
proof of a variation of the Burkholder-Davis-Gundy inequality for the case of
stochastic integrals with respect to real locally square integrable
martingales. Further possible applications and extensions of the method are
outlined.Comment: Published in Statistics and Probability Letters by the Elsevier.
Permanent link: http://dx.doi.org/10.1016/j.spl.2011.01.022 Preliminary
version of this paper appeared on October 27, 2009 as EURANDOM Report
2009-03
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