A limit theorem for singular stochastic differential equations
Анотація
We study the weak limits of solutions to SDEs \[ dX_{n}(t)=a_{n}\big(X_{n}(t)\big)\hspace{0.1667em}dt+dW(t),\] where the sequence $\{a_{n}\}$ converges in some sense to $(c_{-}\mathbb{1}_{x<0}+c_{+}\mathbb{1}_{x>0})/x+\gamma \delta _{0}$. Here $\delta _{0}$ is the Dirac delta function concentrated at zero. A limit of $\{X_{n}\}$ may be a Bessel process, a skew Bessel process, or a mixture of Bessel processes.
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