Does the following equation has a well known weak solution: $$dX_t = \rm{sgn}(X_t)dB^1_t + dB^2_t$$ for independent $B^1$ and $B^2?$ If so does it have unique distribution? The original Tanaka equation can be solved with a simple trick but in this case I could not find any way to get my head around it. Any help is appreciated!
2026-04-01 17:32:14.1775064734
A version of Tanaka equation
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