Uncertainty Propagation in Stochastic Hybrid Systems with Dimension-Varying Resets

Tejaswi K. C.; Taeyoung Lee

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arXiv · 2604.06708

Uncertainty Propagation in Stochastic Hybrid Systems with Dimension-Varying Resets

Tejaswi K. C.·Taeyoung Lee

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Abstract

This paper studies probability density evolution for stochastic hybrid systems with reset maps that change the dimension of the continuous state across modes. Existing Frobenius--Perron formulations typically represent reset-induced probability transfer through boundary conditions, which is insufficient when resets map guard sets into the interior or onto lower-dimensional subsets of another mode. We develop a weak-form formulation in which reset-induced transfer is represented by the pushforward of probability flux across the guard, yielding a unified description for such systems. The proposed framework naturally captures both cases: when the reset decreases dimension, the transferred probability appears as an interior source density, whereas when the reset increases dimension, it generally appears as a singular source supported on a lower-dimensional subset. The approach is illustrated using a stochastic hybrid model in which two particles merge into one and later split back into two, demonstrating how dimension-changing resets lead to source terms beyond classical boundary-condition-based formulations.

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BibTeX RIS

Tejaswi K. C., Taeyoung Lee. 2026-04-08. Uncertainty Propagation in Stochastic Hybrid Systems with Dimension-Varying Resets. https://arxiv.org/abs/2604.06708

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