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arXiv · 2601.21659

The Kolmogorov forward equation for a distributed model of regime-switching diffusions

Alexander S. Bratus·Olga S. Rozanova
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Abstract

For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states continuously distributed over a segment. We demonstrate that there exists a constructive algorithm for solving the Cauchy problem. We then show that for some initial distributions of states, the solution can be found explicitly. We also discuss how a model with a discrete number of hidden states can be approximated by a model with continuously distributed states.

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Alexander S. Bratus, Olga S. Rozanova. 2026-01-29. The Kolmogorov forward equation for a distributed model of regime-switching diffusions. https://arxiv.org/abs/2601.21659

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