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A controlled branching process (CBP) is a modification of the standardBienaym\'e-Galton-Watson process in which the number of progenitors in eachgeneration is determined by a random mechanism. We consider a CBP starting froma random number of initial individuals. The main aim of this paper is toprovide a Feller diffusion approximation for critical CBPs. A similar result byconsidering a fixed number of initial individuals by using operator semigroupconvergence theorems has been previously proved in Sriram at al. (2007). Analternative proof is now provided making use of limit theorems for {random stepprocesses}.

Diffusion approximation of controlled branching processes using limit theorems for random step processes