We study solutions of the irregular Stratonovich SDE $dX = X|^\alpha \circ dB$, $\alpha\in (0, 1)$. In particular we construct solutions spending positive time in 0, describe solutions spending zero time in 0, and show how a particular physically natural solution can be singled out by means of an additional external "ambient" noise.

This talk is based on the joint works with G. Shevchenko (Kiev).