Work

Derivative Formulae and Gradient Estimates for Stochastic Hamiltonian Systems with Jumps

Year: 2026

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.25771

Author: Zhang, Hua

Institution: Jiangxi University of Finance and Economics

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Jiangxi Province

Awards: G1203918405, G176459693, G3832849291

OpenAlex ID: W7214117696

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