Sparad:
| Huvudupphovsmän: | , , , |
|---|---|
| Materialtyp: | Preprint |
| Publicerad: |
2026
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| Ämnen: | |
| Länkar: | https://arxiv.org/abs/2601.12712 |
| Taggar: |
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Innehållsförteckning:
- Many biological systems exhibit multiscale dynamics, where some species occur in high copy numbers while others remain rare. This heterogeneity necessitates hybrid modelling approaches: deterministic models are computationally efficient but inaccurate for low-count species, while fully stochastic simulations are accurate but prohibitively expensive. Hybrid methods like the Jump-Switch-Flow (JSF) algorithm address this by simulating low-count species stochastically and high-count species deterministically. However, selecting regime-switching thresholds to control errors for specific observables remains an open challenge. We develop a principled framework for threshold selection targeting extinction probability. We formalise JSF as a piecewise-deterministic Markov process and derive backward equations for extinction under exact and hybrid dynamics. Near extinction boundaries, complex nonlinear dynamics reduce to tractable time-inhomogeneous linear birth-death processes. This structure yields a rigorous error decomposition based on early and late excursions. Isolating the dominant error term motivates a fast, actionable heuristic. We demonstrate via Monte Carlo studies on a stochastic Lotka-Volterra model that our heuristic reliably upper-bounds empirical errors in extinction probability. This enables users to select the smallest threshold that satisfies a target error tolerance. This work paves the way for principled, efficient multiscale modelling and simulation in stochastic biological systems.