  We construct fractional Brownian motion (fBm), sub-fractional Brownian motion
(sub-fBm), negative sub-fractional Brownian motion (nsfBm) and the odd part of
fBm in the sense of Dzhaparidze and van Zanten (2004) by means of limiting
procedures applied to some particle systems. These processes are obtained for
full ranges of Hurst parameter. Particle picture interpretations of sub-fBm and
nsfBm were known earlier (using a different approach) for narrow ranges of
parameters; the odd part of fBm process had not been given any physical
interpretation at all.
  Our approach consists in representing these processes as $<X(1),1_{[0,t]}>$,
$<X(1),1_{[0,t]}-1_{[-t,0]}>$, $<X(1),1_{[-t,t]}>$, respectively, where X(1) is
an (extended) $S'$-random variable obtained as the fluctuation limit of either
empirical process or the occupation time process of an appropriate particle
system. In fact, our construction is more general, permitting to obtain some
new Gaussian processes, as well as multidimensional random fields. In
particular, we generalize and presumably simplify some results by Hambly and
Jones (2007). We also obtain a new class of $S'$-valued density processes,
containing as a particular case the density process of Martin-L\"of (1976).
