Co-jumps and Markov counting systems in random environments. (English) Zbl 1483.60109
Sadovnichiy, Victor A. (ed.) et al., Contemporary approaches and methods in fundamental mathematics and mechanics. Cham: Springer. Underst. Complex Syst., 277-292 (2021).
Summary: Motivated by the analysis of multi-strain infectious disease data, we provide closed-form transition rates for continuous-time Markov chains that arise from subjecting Markov counting systems to correlated environmental noises. Noise correlation induces co-jumps or counts that occur simultaneously in several counting processes. Such co-jumps are necessary and sufficient for infinitesimal correlation between counting processes of the system. We analyzed such infinitesimal correlation for a specific infectious disease model by randomizing time of Kolmogorov’s Backward system of differential equations based on appropriate stochastic integrals.
For the entire collection see [Zbl 1470.53006].
For the entire collection see [Zbl 1470.53006].
MSC:
| 60J27 | Continuous-time Markov processes on discrete state spaces |
| 60K37 | Processes in random environments |
| 60H05 | Stochastic integrals |
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