A class of Langevin-like equations (non-Markovian processes) are studied in the presence of non-natural boundary conditions. Exact results for all cumulants and the corresponding Kolmogorov hierarchy of distributions are given in terms of our functional approach we previously reported (1997 J. Phys. A: Math. Gen. 30 8427). The generalized Wiener processes - on finite domains - are completely characterized for reflecting and periodic boundary conditions. Some examples are given to show the behaviour of the moments and the probability distributions for different noises. The interplay between the boundary conditions and the structure of the noises is also pointed out.
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Budini et al. (1999) studied this question.
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