A scaling limit of controlled branching processes (Q6540924)

The author studies the continuous branching process with dependent immigration (CBDI) \(\{Y_t,\,t\geqslant0 \}\), which is described as a non-negative solution to the stochastic integral equation given in (1.3) (see the paper). The main results, based on the martingale approach, consists of showing that ``under some mild conditions \(\{Y_k(t):t\geqslant0\}_k\) converges in distribution on \(D([0,\,\infty],\,\mathbb{R}_+)\) to a weak solution of (1.3) with initial value \(Y_0\).''