The theory of imprecise Markov chains has achieved significant progress in recent years. Its applicability, however, is still very much limited, due in large part to the lack of efficient computational methods for calculating higher dimensional models. The high computational complexity shows itself especially in the calculation of the imprecise version of the Kolmogorov backward equation.
The goal of this chapter is to provide a new, more efficient approach for solving the imprecise Kolmogorov backward equation. It is based on the Lipschitz continuity of the solutions of the equation with respect to time, causing the linear programming problems appearing in proximate points of the time interval to have similar optimal solutions. This property is exploited by utilizing the theory of normal cones of convex sets.
Computing Bounds for Imprecise Continuous-Time Markov Chains Using Normal Cones
Space Technol.Proceedings
International Conference on Uncertainty Quantification & Optimisation ; 2020 ; Brussels, Belgium November 17, 2020 - November 20, 2020
Advances in Uncertainty Quantification and Optimization Under Uncertainty with Aerospace Applications ; Chapter : 10 ; 151-171
2021-07-16
21 pages
Article/Chapter (Book)
Electronic Resource
English
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