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Factorization of solutions to generalized Feynman-Kac equations for jump-diffusion models

Victor E. Gluzberg1,* and Yuri A. Katz2,†

  • 1PTC, PTC drive, 1, Haifa 3490002, Israel
  • 2Katz School of Science and Health, Yeshiva University, 205 Lexington Avenue, New York, New York 10016, USA

  • *Contact author: vegluzberg@gmail.com
  • †Contact author: yuri.katz@yu.edu
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Phys. Rev. E 114, 034104 – Published 2 September, 2026

DOI: https://doi.org/10.1103/6sbl-9cwf

Abstract

Standard affine jump-diffusion models treat shocks as increments to the system's state, whereas conventional stochastic resetting models reduce their impact to a full reset of the system's state. Neither model is adequate when diffusion along one of the state components persists, while shocks affect another component. Our study examines a linear system perturbed by two independent additive Markovian components. We demonstrate that in this model the solutions to the generalized Feynman-Kac (GFK) equations describing the expected evolution operator admit an exact factorization to solutions corresponding to separate noise components. Factorizable two-component models are applicable in the real world, particularly in systems where an endogenous background noise persists even when exogenous shocks occur. We show that this decoupling enables a comprehensive description of stylized yield-curve shapes. Furthermore, it allows for the prediction of deviations from exponential Moore's Law trajectories for novel technologies.

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Phys. Rev. E 114, 034104– Published 2 September, 2026
  • Received 14 April 2026
  • Revised 3 August 2026
  • Accepted 7 August 2026
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