A limit theorem for singular stochastic differential equations
Volume 3, Issue 3 (2016), pp. 223–235
Pub. online: 8 November 2016
Type: Research Article
Open Access
Open Access
Received
19 September 2016
19 September 2016
Revised
23 October 2016
23 October 2016
Accepted
23 October 2016
23 October 2016
Published
8 November 2016
8 November 2016
Abstract
We study the weak limits of solutions to SDEs
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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