On the Heterogeneous diffusion process

We consider a Stratonovich stochastic differential equation. We determine solutions of the irregular/singular Stratonovich SDE $dX =|X|^\alpha \circ dB$, $\alpha \in (-1, 1)$, which are strong Markov processes spending zero time in 0. The process $X$ was introduced by Cherstvy et al. in "New Journal of Physics" 15, 2013, under the name of "Heterogeneous diffusion process" and can be seen as the Stratonovich version of the famous Girsanov (Itô) SDE $dX = |X|^\alpha dB$.
This is joint work with G. Shevchenko (Kyiv University), http://arxiv.org/abs/1812.053245324