  The random walk process in a nonhomogeneous medium, characterised by a L\'evy
stable distribution of jump length, is discussed. The width depends on a
position: either before the jump or after that. In the latter case, the density
slope is affected by the variable width and the variance may be finite; then
all kinds of the anomalous diffusion are predicted. In the former case, only
the time characteristics are sensitive to the variable width. %while the former
case resolves itself to a problem with a variable jumping rate, The
corresponding Langevin equation with different interpretations of the
multiplicative noise is discussed. The dependence of the distribution width on
position after jump is interpreted in terms of cognitive abilities and related
to such problems as migration in a human population and foraging habits of
animals.
