  We consider stochastic systems involving general -- non-Gaussian and
asymmetric -- stable processes. The random quantities, either a stochastic
force or a waiting time in a random walk process, explicitly depend on the
position. A fractional diffusion equation corresponding to a master equation
for a jumping process with a variable jumping rate is solved in a diffusion
limit. It is demonstrated that for some model parameters the equation is
satisfied in that limit by the stable process with the same asymptotics as the
driving noise. The Langevin equation containing a multiplicative noise,
depending on the position as a power-law, is solved; the existing moments are
evaluated. The motion appears subdiffusive and the transport depends on the
asymmetry parameter: it is fastest for the symmetric case. A special case of
the one-sided distribution is discussed.
