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Lyapunov functions and Tiers for ergodicity and mixing times of stochastic reaction networks

Banff International Research Station for Mathematical Innovation and Discovery

The Lyapunov-Foster criteria is one of the well known methods for verifying ergodicity of Markov processes. The "Standard Lyapunov function” has played a significant role in the analysis of deterministic reaction networks, especially in regards to deficiency 0 networks. I will provide conditions on reaction networks that guarantee the Standard Lyapunov function satisfies the Lyapunov-Foster criteria. The analysis utilizes hierarchies of intensities and rate functions (Tier structures). I will also provide some special classes of reaction networks satisfying the conditions, thus proving networks in those classes are positive recurrent. I will also provide some results pertaining to the mixing times of reaction networks.

Mathematics; Dynamical systems and ergodic theory; Probability theory and stochastic processes; Mathematical biology

video/mp4

Author affiliation: University of Wisconsin-Madison

2017-12-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63828

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/