A transition probability approach is used to study transport caused by linear instabilities in the real (coordinate) and velocity spaces. The general non-Markovian Fokker–Planck treatment is used to derive the diffusion coefficients. The Dupree–Weinstock renormalized diffusion is reproduced in the Markovian limit. For transport in real space, the non-Markovian diffusion coefficient which is part of one of the transport models used in predicting the performance of the International Thermonuclear Experimental Reactor, [D.R. Mikkelsen, G. Bateman, D. Boucher et al., Proceedings of the Sixteenth IAEA Fusion Energy Conference, Yokohama 1998 (IAEA, Vienna, 1999) Paper IAEA-CN-69/ITER P1/08], is reproduced in a more systematic way.
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