论文标题
Burkholder-Davis-Gundy不平等的概括
A generalisation of the Burkholder-Davis-Gundy inequalities
论文作者
论文摘要
{考虑一个càdlàg本地martingale $ m $带方括号$ [m] $。在本文中，我们提供了上限和下限，以期在任何停止时间$τ$和$ q \ ge 2 $的$ {\ mathbb e}类型$ {\ mathbb e} [m]^{q/2}_τ$中，就可预测的过程而言。可以将此结果视为Burkholder-Davis-Gundy类型的不平等现象，因为它可以用来将最大运行$ | M^*|^Q $的期望与对$ M $相关跳跃相关的相关权力的双重预期预期的期望联系起来。还讨论了一类中等功能的情况。
{Consider a càdlàg local martingale $M$ with square brackets $[M]$. In this paper, we provide upper and lower bounds for expectations of the type ${\mathbb E} [M]^{q/2}_τ$, for any stopping time $τ$ and $q\ge 2$, in terms of predictable processes. This result can be thought of as a Burkholder-Davis-Gundy type inequality in the sense that it can be used to relate the expectation of the running maximum $|M^*|^q$ to the expectation of the dual previsible projections of the relevant powers of the associated jumps of $M$. The case for a class of moderate functions is also discussed.
