随机积分的代数多项式和矩
Algebraic polynomials and moments of stochastic integrals
摘要：
提出了一种证明随机积分矩估计的代数方法。该方法使用定性性质的根代数多项式从某些一般类。作为应用，我们给出了关于实局部平方可积鞅的随机积分的Burkholder-Davis-Gundy不等式的一个变形的新证明.进一步可能的应用和扩展的方法进行了概述。
英文摘要：
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.
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