We provide transition rates for Markov counting systems subject to correlated environmental noises motivated by multi-strain disease models. Such noises induce simultaneous counts, which can help model infinitesimal count correlation (regardless of whether such correlation is due to correlated noises).
Convergence to extremal processes in random environments and extremal ageing in SK models
Random walks in random environments without ellipticity
Timescales of population rarity and commonness in random environments
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