Numerical approximation for functionals of reflecting diffusion processes
SIAM Journal on Applied Mathematics
Reconstruction of switching thresholds in piecewise-affine models of genetic regulatory networks
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Computational methods for reachability analysis of stochastic hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Reachability Analysis for Stochastic Hybrid Systems Using Multilevel Splitting
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Multilevel splitting for reachability analysis of stochastic hybrid systems
Proceedings of the 2010 Conference on Grand Challenges in Modeling & Simulation
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Modeling and simulation of biochemical systems are important tasks because they can provide insights into complicated systems where traditional experimentation is expensive or impossible. Stochastic hybrid systems are an ideal modeling paradigm for biochemical systems because they combine continuous and discrete dynamics in a stochastic framework. Simulation of these systems is difficult because of the inherent error which is introduced near the boundaries. In this work we develop a method for stochastic hybrid system simulation that explicitly considers switching and reflective boundaries. We also present a case study of the water/electrolyte balance system in humans and provide simulation results to demonstrate the usefulness of the improved simulation techniques.