The Schrödinger Bridge Problem for Jump Diffusions with Regime Switching
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arXiv
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| Format: | Preprint |
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2025
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| author | Zlotchevski, Andrei Chen, Linan |
| author_facet | Zlotchevski, Andrei Chen, Linan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_06079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Schrödinger Bridge Problem for Jump Diffusions with Regime Switching Zlotchevski, Andrei Chen, Linan Probability Optimization and Control 35Q93, 45K05, 49J20, 60H10, 60H30, 60J25, 93E20, 94A17 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. |
| title | The Schrödinger Bridge Problem for Jump Diffusions with Regime Switching |
| topic | Probability Optimization and Control 35Q93, 45K05, 49J20, 60H10, 60H30, 60J25, 93E20, 94A17 |
| url | https://arxiv.org/abs/2511.06079 |