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

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.