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Stochastic population dynamics under regime switching. (English) Zbl 1113.92052
Summary: We develop a new stochastic population model under regime switching. Our model takes both white and color environmental noises into account. We show that the white noise suppresses explosions in population dynamics. Moreover, from the point of population dynamics, our new model has more desired properties than some existing stochastic population models. In particular, we show that our model is stochastically ultimately bounded.

MSC:
92D25 Population dynamics (general)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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