Heterogeneous diffusion: uniqueness, non-uniqueness, and selection

We study the irregular Stratonovich SDE $dX =|X|^\alpha \circ dB$,

$\alpha\in (0, 1)$ and construct solutions that spend positive time in 0, characterize 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) and J. Cardona (Jena).

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