Large deviations for multi-scale regime-switching jump diffusion systems (Q2099243)

The authors prove a large-deviation principle for jump-diffusion processes with coefficients (drift, diffusion, jump kernel) depending on an additional Markov chain in the regime of small noise (diffusion, Lévy) and a fast environment (Markov chain). The rate function has a variational representation as a minimization problem with terms representing the diffusive and both jump-noises. The method of the proof is a generalization of the weak convergence approach to large deviation developed by \textit{A. Budhiraja} et al. [Electron. J. Probab. 23, Paper No. 112, 33 p. (2018; Zbl 1402.60030)].