2025/11/08 by Zlotchevski, Andrei, Chen, Linan · 1 citation
Economics, Econometrics and Finance · Neuroscience · Physics and Astronomy · #35Q93 #45K05 #49J20 #60H10 #60H30 #60J25 #93E20 #94A17 #FOS: Mathematics #Neural dynamics and brain function #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #stochastic dynamics and bifurcation
paper · doi:10.48550/arxiv.2511.06079
openalex publication_date 2025/11/08 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28
The Schrödinger bridge problem (SBP) aims at finding the measure P on a certain path space which possesses the desired state-space distributions ρ0 at time 0 and ρT at time T while minimizing the KL divergence from a reference path measure R. This work focuses on the SBP in the case when R is the path measure of a jump diffusion with regime switching, which is a Markov process that combines the dynamics of a jump diffusion with interspersed discrete events representing changing environmental states. To the best of our knowledge, the SBP in such a setting has not been previously studied. In this paper, we conduct a comprehensive analysis of the dynamics of the SBP solution P in the regime-switching jump-diffusion setting. In particular, we show that P is again a path measure of a regime-switching jump diffusion; under proper assumptions, we establish various properties of P from both a stochastic calculus perspective and an analytic viewpoint. In addition, as an demonstration of the general theory developed in this work, we examine a concrete unbalanced SBP (uSBP) from the angle of a regime-switching SBP, where we also obtain novel results in the realm of uSBP.