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We consider a branching system consisting of particles moving according to aMarkov family in $\Rd$ and undergoing subcritical branching with a constantrate $V>0$. New particles immigrate to the system according to homogeneousspace-time Poisson random field. The process of the fluctuations of therescaled occupation time is studied with very mild assumptions on the Markovfamily. In this general setting a functional central limit theorem is proved.The subcriticality of the branching law is crucial for the limit behaviour andin a sense overwhelms the properties of the particles' motion. It is for thisreason that the limit is the same for all dimensions and can be obtained for awide class of Markov processes. Another consequence is the form of the limit -$\SP$-valued Wiener process with a simple temporal structure and a complicatedspatial one. This behaviour contrasts sharply with the case of criticalbranching systems.

Occupation times of subcritical branching immigration system with Markov motions