A limit theorem for singular stochastic differential equations
Abstract
We study the weak limits of solutions to SDEs \[dXn(t)=an(Xn(t))\,dt+dW(t),\] where the sequence \an\ converges in some sense to (c- 1-4.5mulx<0+c+ 1-4.5mulx>0)/x+γδ0. Here δ0 is the Dirac delta function concentrated at zero. A limit of \Xn\ may be a Bessel process, a skew Bessel process, or a mixture of Bessel processes.
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