Consider the SDE $$ d X_t = (- |B_t| f(X_t) +2|B_t| - 2 f(X_t)) dt. $$ Here, $f$ is $1$-periodic with $f(x)=x$ for $x\in[0,1)$, $B_t$ is Brownian Motion. Then how to prove the existence of the density of $(X_t,|B_t|)$? We can suppose that the initial data is a dirac-mass.
2026-04-01 15:53:09.1775058789
How to prove the existence of the density of diffusion process with discontinuous drift?
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