I heard "Feller made a famous mistake in 1954 and fixed by A.D. Wentell in 1959" from one lecture. There is no further explain what is that mistake? Is there someone know it? Is it possible to explain a little bit it?



What is famous mistake made by Feller?
For reference, the two papers are


[1] W. Feller. [Diffusion processes in one dimension,](https://doi.org/10.1090/S0002-9947-1954-0063607-6%20) Trans. Amer. Math. Soc. **97**, 1-31 (1954).  

[2] A. D. Wentzell. [On boundary conditions for multidimensional diffusion processes,](https://doi.org/10.1137/1104014) Theor. Probability Appl. **4**, 164-177 (1959).


Differential operators with boundary conditions containing diffusion terms were introduced by Feller [1] for one-dimensional diffusion and by Wentzell [2] for higher dimensions.


My best guess to what is going on is that the the lecturer was referring to the limitation to one dimension in Feller's 1954 work, a limitation removed by Wentzell's 1959 paper. I am not aware of any error in [1].


