Existence and uniqueness of reflecting diffusions in cusps
2018
We consider stochastic differential equations with (oblique) reflection in a $2$-dimensional domain that has a cusp at the origin, i..e. in a neighborhood of the origin has the form $\{(x_1,x_2):00$, $i=1,2$, and $e^{*}_1>0$, we prove weak existence and uniqueness of the solution starting at the origin and strong existence and uniqueness starting away from the origin.
Our proof uses a new scaling result and a coupling argument.
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