 Large deviations for Markov processes with switching and homogenisation via Hamilton–Jacobi–Bellman equationsSerena Della Corte and Richard C. Kraaij Stochastic Processes and their Applications, 2024, vol. 170, issue C Abstract: We consider the context of molecular motors modelled by a diffusion process driven by the gradient of a weakly periodic potential that depends on an internal degree of freedom. The switch of the internal state, that can freely be interpreted as a molecular switch, is modelled as a Markov jump process that depends on the location of the motor. Rescaling space and time, the limit of the trajectory of the diffusion process homogenises over the periodic potential as well as over the internal degree of freedom. Around the homogenised limit, we prove the large deviation principle of trajectories with a method developed by Feng and Kurtz based on the analysis of an associated Hamilton–Jacobi–Bellman equation with an Hamiltonian that here, as an innovative fact, depends on both position and momenta. Keywords: Large deviations; Switching Markov process; Hamilton–Jacobi equation; Viscosity solutions; Comparison principle (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:170:y:2024:i:c:s0304414924000073 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2024.104301 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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