论文标题
耗时的瞬间半明天，跳高跳跃
Moment bounds for dissipative semimartingales with heavy jumps
论文作者
论文摘要
在本文中，我们表明，如果iTô-semimartingale $ x $的大跳跃具有有限的$ p $ -p $ - amment，$ p> 0 $，则其漂移的径向部分由$ - | x |^κ$主导，对于某些$κ\ geq-q q q q q Q Q-q Q-q-q -1 $，余额$ p+κ> $ prable $ p+κ> $ \ Mathbf {e} | x_t |^{p_x} <\ infty $ in（0，p+κ-1）$。上限$ P+κ-1 $通常是最佳的。该证明是基于Lyapunov函数方法扩展到Semimartingale框架的。在本文中获得的均匀力矩估计值对于分析Lévy驱动的随机微分方程和Lévy驱动的多尺度系统的Ergodic特性是必不可少的。
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 $-|X|^κ$ for some $κ\geq -1$, and the balance condition $p+κ>1$ holds true, then under some further natural technical assumptions $\sup_{t\geq 0} \mathbf{E} |X_t|^{p_X}<\infty$ for each $p_X\in(0,p+κ-1)$. The upper bound $p+κ-1$ 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.
