Diffusion approximation of evolutionary systems with equilibrium in asymptotic split phase space
Vladimir Semenovich Korolyuk, Nikolaos Limnios · Theory of Probability and Mathematical Statistics · 2005
In this paper we consider an additive functional of a Markov process with locally independent increments switched by a Markov process. For this functional, we obtain nonhomogeneous diffusion approximation results without balance condition on the drift parameter. A more general diffusion approximation result is obtained in the case of an asymptotic split phase space of the switching Markov process.