A transition probability approach is used to study transport caused by line
ar instabilities in the real (coordinate) and velocity spaces. The general
non-Markovian Fokker-Planck treatment is used to derive the diffusion coeff
icients. The Dupree-Weinstock renormalized diffusion is reproduced in the M
arkovian limit. For transport in real space, the non-Markovian diffusion co
efficient which is part of one of the transport models used in predicting t
he performance of the International Thermonuclear Experimental Reactor, [D.
R. Mikkelsen, G. Bateman, D. Boucher et al., Proceedings of the Sixteenth I
AEA Fusion Energy Conference, Yokohama 1998 (IAEA, Vienna, 1999) Paper IAEA
-CN-69/ITER P1/08], is reproduced in a more systematic way. (C) 1999 Americ
an Institute of Physics. [S1070-664X(99)00206-2].