Print Email Facebook Twitter Large Deviations for Finite State Markov Jump Processes with Mean-Field Interaction Via the Comparison Principle for an Associated Hamilton–Jacobi Equation Title Large Deviations for Finite State Markov Jump Processes with Mean-Field Interaction Via the Comparison Principle for an Associated Hamilton–Jacobi Equation Author Kraaij, R.C. (TU Delft Applied Probability) Date 2016 Abstract We prove the large deviation principle (LDP) for the trajectory of a broad class of finite state mean-field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well as Curie–Weiss spin flip dynamics with singular jump rates. The main step in the proof of the LDP, which is of independent interest, is the proof of the comparison principle for an associated collection of Hamilton–Jacobi equations. Additionally, we show that the LDP provides a general method to identify a Lyapunov function for the associated McKean–Vlasov equation. Subject Large deviationsNon-linear jump processesHamilton–Jacobi equationViscosity solutionsComparison principle To reference this document use: http://resolver.tudelft.nl/uuid:2913605a-4ad4-4b95-ac76-3ca8d9396493 DOI https://doi.org/10.1007/s10955-016-1542-8 ISSN 0022-4715 Source Journal of Statistical Physics, 164 (2), 321-345 Part of collection Institutional Repository Document type journal article Rights © 2016 R.C. Kraaij Files PDF 10.1007_s10955_016_1542_8.pdf 680.53 KB Close viewer /islandora/object/uuid:2913605a-4ad4-4b95-ac76-3ca8d9396493/datastream/OBJ/view