Large deviations theory for Markov jump models of chemical reaction networks
Abstract
We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it we further establish the corresponding Wentzell-Freidlin (W-F) (infinite time horizon) asymptotic theory. These results apply to jump Markov processes that model the dynamics of chemical reaction networks under mass action kinetics, on a microscopic scale. We provide natural sufficient topological conditions for the applicability of our LDP and W-F results. This then justifies the computation of non-equilibrium potential and exponential transition time estimates between different attractors in the large volume limit, for systems that are beyond the reach of standard chemical reaction network theory.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2017
- DOI:
- 10.48550/arXiv.1701.02126
- arXiv:
- arXiv:1701.02126
- Bibcode:
- 2017arXiv170102126A
- Keywords:
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- Mathematics - Probability;
- Mathematics - Dynamical Systems;
- Quantitative Biology - Molecular Networks;
- 60F10;
- 80A30 (primary);
- 37B25;
- 60J75 (secondary)