{"ID":2844688,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.06079","arxiv_id":"2511.06079","title":"The Schrödinger Bridge Problem for Jump Diffusions with Regime Switching","abstract":"The Schrödinger bridge problem (SBP) aims at finding the measure $\\hat{\\mathbf{P}}$ on a certain path space which possesses the desired state-space distributions $ρ_0$ at time $0$ and $ρ_T$ at time $T$ while minimizing the KL divergence from a reference path measure $\\mathbf{R}$. This work focuses on the SBP in the case when $\\mathbf{R}$ 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 $\\hat{\\mathbf{P}}$ in the regime-switching jump-diffusion setting. In particular, we show that $\\hat{\\mathbf{P}}$ is again a path measure of a regime-switching jump diffusion; under proper assumptions, we establish various properties of $\\hat{\\mathbf{P}}$ 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.","short_abstract":"The Schrödinger bridge problem (SBP) aims at finding the measure $\\hat{\\mathbf{P}}$ on a certain path space which possesses the desired state-space distributions $ρ_0$ at time $0$ and $ρ_T$ at time $T$ while minimizing the KL divergence from a reference path measure $\\mathbf{R}$. This work focuses on the SBP in the cas...","url_abs":"https://arxiv.org/abs/2511.06079","url_pdf":"https://arxiv.org/pdf/2511.06079v1","authors":"[\"Andrei Zlotchevski\",\"Linan Chen\"]","published":"2025-11-08T17:23:31Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[\"Diffusion Model\"]","has_code":false}