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4 hours ago comment added Akira @RobertWegner Maybe you can check Theorem 1.1(2) of this paper.
4 hours ago comment added Robert Wegner Thank you! That's a good start. Only problem is I am working with a Brownian motion conditioned to stay in [-R, R], so there is a singular drift term, i.e. not Lipschitz continuous. But maybe I will find a way to still apply this argument!
4 hours ago history answered user479223 CC BY-SA 4.0