发表机构
Jiangxi University of Finance and Economics（江西财经大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对Lévy过程驱动的随机哈密顿系统，利用带跳跃的Malliavin微积分中的lent particle方法，建立了显式的Bismut--Elworthy--Li型导数公式和梯度估计，将退化系统的结果推广到非局部跳跃情形，填补了文献空白。
AI 中文摘要
本文研究由Lévy过程驱动的随机哈密顿系统。通过利用Bouleau和Denis在带跳跃的Malliavin微积分框架中发展的lent particle方法，我们为相关的马尔可夫半群建立了显式的Bismut--Elworthy--Li型导数公式，以及相应的梯度估计。主要新颖之处在于将布朗运动驱动的退化系统的已知结果推广到带跳跃的非局部情形，其中纯跳跃噪声的存在和系数的退化性带来了实质性困难。我们的方法为这类非局部退化算子提供了系统的处理，填补了跳跃型随机哈密顿系统导数公式文献中的空白。
英文摘要
This paper is concerned with stochastic Hamiltonian systems driven by Lévy processes. By employing the lent particle method developed by Bouleau and Denis in the framework of Malliavin calculus with jumps, we establish an explicit Bismut--Elworthy--Li type derivative formula for the associated Markov semigroup, as well as corresponding gradient estimates. The main novelty lies in extending the known results for Brownian-motion-driven degenerate systems to the nonlocal setting with jumps, where the presence of a pure jump noise and the degeneracy of the coefficients pose substantial difficulties. Our approach provides a systematic treatment of such nonlocal degenerate operators and fills a gap in the literature on derivative formulae for jump-type stochastic Hamiltonian systems.
Comments29 pages
