Approximation of SDEs by population-size-dependent Galton-Watson processes
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A certain class of stochastic differential equations, containing the Cox-Ingersoll-Ross model and the geometric Brownian motion, is considered. The corresponding solutions are approximated weakly by discrete-time population-size-dependent Galton-Watson processes with immigration. The long-time behavior of the limiting processes is also investigated.
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stochastic differential equation, Galton-Watson process, populationsize-dependent branching, weak convergence, martingale problem, Doob-Meyer decomposition, Cox-Ingersoll-Ross model