On the non-uniqueness of the limit points of diffusions with a small parameter
Tzuu-Shuh Chiang, Chii-Ruey Hwang · Stochastics · 1983
Let P∊ be the iaw of the 1-dim diffusion with generator where a > 0 and a, b are bounded continuous functions. We use a Tauberian theorem to construct an example that {P∊}∊>0 fails to have an unique limit point if b does not satisfy the Lipschitz condition.