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PreprintarXiv licencearXiv

Linear Response Theory for Jump-Driven Stochastic Systems: Transient Statistics and Escape Dynamics

  • Qingyan Meng
  • Jinqiao Duan
  • Valerio Lucarini
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Abstract

In this paper, we develop a linear response theory for a class of stochastic differential equations driven by jump processes. We investigate the response of the system to small time-dependent perturbations from three complementary perspectives: probability density functions, mean exit times, and escape probabilities. By performing perturbation analyses of the corresponding forward and backward Kolmogorov equations, we derive the first-order response equations governing these statistical quantities and establish explicit linear response formulas, which characterize the sensitivity of the evolution of the probability distribution and the escape behavior of the system to variations in its coefficients.

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Cite

BibTeXRIS
BibTeX
@misc{meng2026linear,
  title = {{Linear Response Theory for Jump-Driven Stochastic Systems: Transient Statistics and Escape Dynamics}},
  author = {Qingyan Meng and Jinqiao Duan and Valerio Lucarini},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12013},
  eprint = {2609.12013},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12013},
}
RIS
TY  - UNPB
TI  - Linear Response Theory for Jump-Driven Stochastic Systems: Transient Statistics and Escape Dynamics
AU  - Qingyan Meng
AU  - Jinqiao Duan
AU  - Valerio Lucarini
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.12013
UR  - https://arxiv.org/abs/2609.12013
AB  - In this paper, we develop a linear response theory for a class of stochastic differential equations driven by jump processes. We investigate the response of the system to small time-dependent perturbations from three complementary perspectives: probability density functions, mean exit times, and escape probabilities. By performing perturbation analyses of the corresponding forward and backward Kolmogorov equations, we derive the first-order response equations governing these statistical quantities and establish explicit linear response formulas, which characterize the sensitivity of the evolution of the probability distribution and the escape behavior of the system to variations in its coefficients.
ER  -