  We consider the limit behavior of a one-dimensional random walk with unit
jumps whose transition probabilities are modified every time the walk hits
zero. The invariance principle is proved in the scheme of series where the size
of modifications depends on the number of series. For the natural scaling of
time and space arguments the limit process is (i) a Brownian motion if
modifications are "small", (ii) a linear motion with a random slope if
modifications are "large", and (iii) the limit process satisfies an SDE with a
local time of unknown process in a drift if modifications are "moderate".
