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We focus on the population dynamics driven by two classes of truncated $\alpha$-stable processes with Markovian switching. Almost necessary and sufficient conditions for the ergodicity of the proposed models are provided. Also, these results illustrate the impact on ergodicity and extinct conditions as the parameter $\alpha$ tends to 2.

This work is concerned with a class of mean-field models given by a switching diffusion with a continuous-state-dependent switching process. Focusing on asymptotic properties, the regularity or nonexplosiveness, Feller continuity, and strong Feller continuity are established by means of introducing certain auxiliary processes and by making use of the truncations. Based on these results, exponential ergodicity is obtained under the Foster–Lyapunov drift conditions. By virtue of the coupling methods, the strong ergodicity or uniform ergodicity in the sense of convergence in the variation norm is established for the mean-field model with a Markovian switching process. Besides this, several examples are presented for demonstration and illustration.

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Population dynamics driven by truncated stable processes with Markovian switching

Asymptotic Properties of a Mean-Field Model with a Continuous-State-Dependent Switching Process

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2 results

Population dynamics driven by truncated stable processes with Markovian switching

Asymptotic Properties of a Mean-Field Model with a Continuous-State-Dependent Switching Process