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undeleted this answer after getting a clarification from the post author
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Todd Trimble
Todd Trimble
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For reference, the two papers are

[1] W. Feller. Diffusion processes in one dimension, Trans. Amer. Math. Soc. 97, 1-31 (1954).
[2] A. D. Wentzell. On boundary conditions for multidimensional diffusion processes, 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. I am not aware of any error in [1]. Perhaps

My best guess to what is going on is that the lecturer in the OPlecturer 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].

For reference, the two papers are

[1] W. Feller. Diffusion processes in one dimension, Trans. Amer. Math. Soc. 97, 1-31 (1954).
[2] A. D. Wentzell. On boundary conditions for multidimensional diffusion processes, 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. I am not aware of any error in [1]. Perhaps the lecturer in the OP was referring to the limitation to one dimension in Feller's work?

For reference, the two papers are

[1] W. Feller. Diffusion processes in one dimension, Trans. Amer. Math. Soc. 97, 1-31 (1954).
[2] A. D. Wentzell. On boundary conditions for multidimensional diffusion processes, 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].

Post Undeleted by Todd Trimble
Mod Converts to Comment
Post Deleted by Asaf Karagila♦
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Carlo Beenakker
Carlo Beenakker
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For reference, the two papers are

[1] W. Feller. Diffusion processes in one dimension, Trans. Amer. Math. Soc. 97, 1-31 (1954).
[2] A. D. Wentzell. On boundary conditions for multidimensional diffusion processes, 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. I am not aware of any error in [1]. Perhaps the lecturer in the OP was referring to the limitation to one dimension in Feller's work?