In this paper we show that if large jumps of an Itô-semimartingale $X$ have a finite $p$-moment, $p>0$, the radial part of its drift is dominated by $-{\left|X\right|}^{\kappa }$ for some $\kappa \ge -1$, and the balance condition $p+\kappa >1$ holds true, then under some further natural technical assumptions one has ${sup}_{t\ge 0}\mathbf{E}{\left|X_t\right|}^{p_X}<\infty$ for each $p_X\in (0,p+\kappa -1)$. The upper bound $p+\kappa -1$ is generically optimal. The proof is based on the extension of the method of Lyapunov functions to the semimartingale framework. The uniform moment estimates obtained in this paper are indispensable for the analysis of ergodic properties of Lévy driven stochastic differential equations and Lévy driven multi-scale systems.

在本文中，我们表明如果 Itô-semimartingale 的大跳跃 $X$ 有一个有限的 $磷$-片刻， $磷>0$，其漂移的径向部分由 $-{\left|X\right|}^{\kappa }$ 对于一些 $\kappa \ge -1$, 平衡条件 $磷+\kappa >1$ 成立，然后在一些进一步的自然技术假设下 ${超}_{吨\ge 0}\mathbf{乙}{\left|X_{吨}\right|}^{{磷}_X}<\infty$ 对于每个 ${磷}_X\in (0,磷+\kappa -1)$. 上限$磷+\kappa -1$一般是最优的。证明是基于李雅普诺夫函数方法对半鞅框架的扩展。本文获得的一致矩估计对于分析 Lévy 驱动的随机微分方程和 Lévy 驱动的多尺度系统的遍历性质是必不可少的。