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Title:聽The Schrodinger bridge problem for regime-switching jump diffusions and its applications to the unbalanced problem.

Abstract:聽The Schrodinger bridge problem (SBP) seeks to find the measure on a certain path space which interpolates between state-space distributions at time 0 and at time T while minimizing the KL divergence (relative entropy) to a reference measure. With nearly a century of research and lying in the intersection of stochastic analysis, optimal transport, and stochastic control, the SBP provides a mathematical framework for incorporating new observational data into an existing model of a dynamical system or for "steering" the system towards a desired outcome. In this work, we extend the known theory about the SBP for diffusions to the setting of regime-switching jump diffusions, and we apply it to study the unbalanced SBP, where the distribution at time T is a sub-probability measure.