Continuous Time Mixed State Branching Processes and Stochastic Equations

Shukai Chen; Zenghu Li

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arXiv · 2104.12960

Continuous Time Mixed State Branching Processes and Stochastic Equations

Shukai Chen·Zenghu Li

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Abstract

A continuous time mixed state branching process is constructed as the scaling limits of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic equation system we derive the distribution of local jumps and the exponential ergodicity in Wasserstein-type distances of the transition semigroup is given. Meanwhile, we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.

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Shukai Chen, Zenghu Li. 2021-04-27. Continuous Time Mixed State Branching Processes and Stochastic Equations. https://arxiv.org/abs/2104.12960

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